Monthly Archives: November 2014

What Can Replace Space-Time?

Nima Arkani-Hamed is famous for believing that space-time is doomed, that as physicists we will have to abandon the concepts of space and time if we want to find the ultimate theory of the universe. He’s joked that this is what motivates him to get up in the morning. He tends to bring it up often in talks, both for physicists and for the general public.

The latter especially tend to be baffled by this idea. I’ve heard a lot of questions like “if space-time is doomed, what could replace it?”

In the past, Nima and I both tended to answer this question with a shrug. (Though a more elaborate shrug in his case.) This is the honest answer: we don’t know what replaces space-time, we’re still looking for a good solution. Nima’s Amplituhedron may eventually provide an answer, but it’s still not clear what that answer will look like. I’ve recently realized, though, that this way of responding to the question misses its real thrust.

When people ask me “what could replace space-time?” they’re not asking “what will replace space-time?” Rather, they’re asking “what could possibly replace space-time?” It’s not that they want to know the answer before we’ve found it, it’s that they don’t understand how any reasonable answer could possibly exist.

I don’t think this concern has been addressed much by physicists, and it’s a pity, because it’s not very hard to answer. You don’t even need advanced physics. All you need is some fairly old philosophy. Specifically we’ll use concepts from metaphysics, the branch of philosophy that deals with categories of being.

Think about your day yesterday. Maybe you had breakfast at home, drove to work, had a meeting, then went home and watched TV.

Each of those steps can be thought of as an event. Each event is something that happened that we want to pay attention to. You having breakfast was an event, as was you arriving at work.

These events are connected by relations. Here, each relation specifies the connection between two events. There might be a relation of cause-and-effect, for example, between you arriving at work late and meeting with your boss later in the day.

Space and time, then, can be seen as additional types of relations. Your breakfast is related to you arriving at work: it is before it in time, and some distance from it in space. Before and after, distant in one direction or another, these are all relations between the two events.

Using these relations, we can infer other relations between the events. For example, if we know the distance relating your breakfast and arriving at work, we can make a decent guess at another relation, the difference in amount of gas in your car.

This way of viewing the world, events connected by relations, is already quite common in physics. With Einstein’s theory of relativity, it’s hard to say exactly when or where an event happened, but the overall relationship between two events (distance in space and time taken together) can be thought of much more precisely. As I’ve mentioned before, the curved space-time necessary for Einstein’s theory of gravity can be thought of equally well as a change in the way you measure distances between two points.

So if space and time are relations between events, what would it mean for space-time to be doomed?

The key thing to realize here is that space and time are very specific relations between events, with very specific properties. Some of those properties are what cause problems for quantum gravity, problems which prompt people to suggest that space-time is doomed.

One of those properties is the fact that, when you multiply two distances together, it doesn’t matter which order you do it in. This probably sounds obvious, because you’re used to multiplying normal numbers, for which this is always true anyway. But even slightly more complicated mathematical objects, like matrices, don’t always obey this rule. If distances were this sort of mathematical object, then multiplying them in different orders could give slightly different results. If the difference were small enough, we wouldn’t be able to tell that it was happening in everyday life: distance would have given way to some more complicated concept, but it would still act like distance for us.

That specific idea isn’t generally suggested as a solution to the problems of space and time, but it’s a useful toy model that physicists have used to solve other problems.

It’s the general principle I want to get across: if you want to replace space and time, you need a relation between events. That relation should behave like space and time on the scales we’re used to, but it can be different on very small scales (Big Bang, inside of Black Holes) and on very large scales (long-term fate of the universe).

Space-time is doomed, and we don’t know yet what’s going to replace it. But whatever it is, whatever form it takes, we do know one thing: it’s going to be a relation between events.

Research or Conference? Can’t it be both?

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“If you’re there for two months, for sure you’ll be doing research.”

I wanted to be snarky. I wanted to point out that, as a theoretical physicist, I do research wherever I go. I wanted to say that I even did research on the drive over. (This may not have been true, I think I mostly thought about Magic the Gathering cards.)

More than any of those, though, I wanted to get my travel visa. So instead I said,

“That’s fair.”

“Mmhmm, that’s fair.” Looking down at the invitation letter, she triumphantly pointed to the name of the inviting institution: “South American Institute for Fundamental Research.”

A bit of background: I’m going to Brazil this winter. Partly, this is because winter in Canada is not especially desirable, but it’s also because Sao Paulo’s International Center for Theoretical Physics is running a Program on Integrability, the arcane set of techniques that seeks to bypass the approximate perturbations we often use in particle physics and find full, exact results.

What do I mean by a Program? It’s not the sort of scientific program I’ve talked about before, though the ideas are related. When an institute holds a Program, they’re declaring a theme. For a certain length of time (generally from a few months to a whole semester), there will be a large number of talks at the institute focused on some particular scientific theme. The institute invites people from all over the world who work on that theme. Those people are there to give and attend talks, but they’re also there to share ideas with each other, to network and collaborate and do research.

This is where things get tricky. See, Brazil has multiple types of visas. A Tourist Visa can be used, among other things, for attending a scientific conference. On the other hand, someone coming to Brazil to do research uses Visa 1.

A Program is essentially a long conference…but it’s also an opportunity to do research. So are most short conferences, though! In theoretical physics we have workshops, short conferences explicitly focused on collaboration and research, but even if a conference isn’t a workshop you can bet that we’ll be doing some research there, for sure. We don’t need labs, and some of us don’t even need computers, research can happen whenever the inspiration strikes. The distinction between conferences and research, from our perspective, is an arbitrary one.

In physics, we like to cut through this sort of ambiguity by looking at what’s really important. I wanted to figure out what about research makes the Brazilian government use a different visa for it, whether it was about motivating people to enter the country for specific reasons or tracking certain sorts of activities. I wanted to understand that, because it would let me figure out whether my own research fell under those reasons, and thus figure out objectively which type of visa I ought to have.

I wanted to ask about all of this…but more than any of that, I wanted to get my travel visa. So I applied for the visa they told me to, and left.

Misleading Headlines and Tacky Physics, Oh My!

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It’s been making the rounds on the blogosphere (despite having come out three months ago). It’s probably showed up on your Facebook feed. It’s the news that (apparently) one of the biggest discoveries of recent years may have been premature. It’s….

The Huffington Post writing a misleading headline to drum up clicks!

The article linked above is titled “Scientists Raise Doubts About Higgs Boson Discovery, Say It Could Be Another Particle”. And while that is indeed technically all true, it’s more than a little misleading.

When the various teams at the Large Hadron Collider announced their discovery of the Higgs, they didn’t say it was exactly the Higgs predicted by the Standard Model. In fact, it probably shouldn’t be: most of the options for extending the Standard Model, like supersymmetry, predict a Higgs boson with slightly different properties. Until the Higgs is measured more precisely, these slightly different versions won’t be ruled out.

Of course, “not ruled out” is not exactly newsworthy, which is the main problem with this article. The Huffington Post quotes a paper that argues, not that there is new evidence for an alternative to the Higgs, but simply that one particular alternative that the authors like hasn’t been ruled out yet.

Also, it’s probably the tackiest alternative out there.

The theory in question is called Technicolor, and if you’re imagining a certain coat then you may have an idea of how tacky we’re talking.

Any Higgs will do…

To describe technicolor, let’s take a brief aside and talk about the colors of quarks.

Rather than having one type of charge going from plus to minus like Electromagnetism, the Strong Nuclear Force has three types of charge, called red, green, and blue. Quarks are charged under the strong force, and can be red, green, or blue, while the antimatter partners of quarks have the equivalent of negative charges, anti-red, anti-green, and anti-blue. The strong force binds quarks together into protons and neutrons. The strong force is also charged under itself, which means that not only does it bind quarks together, it also binds itself together, so that it only acts at very very short range.

In combination, these two facts have one rather surprising consequence. A proton contains three quarks, but a proton’s mass is over a hundred times the total mass of three quarks. The same is true of neutrons.

The reason why is that most of the mass isn’t coming from the quarks, it’s coming from the strength of the strong force. Mass, contrary to what you might think, isn’t fundamental “stuff”. It’s just a handy way of talking about energy that isn’t due to something we can easily see. Particles have energy because they move, but they also have energy due to internal interactions, as well as interactions with other fields like the Higgs field. While a lone quark’s mass is due to its interaction with the Higgs field, the quarks inside a proton are also interacting with each other, gaining enormous amounts of energy from the strong force trapped within. That energy, largely invisible from an outside view, contributes most of what we see as the mass of the proton.

Technicolor asks the following: what if it’s not just protons and neutrons? What if the mass of everything, quarks and electrons and the W and Z bosons, was due not truly to the Higgs, but to another force, like the strong force but even stronger? The Higgs we think we saw at the LHC would not be fundamental, but merely a composite, made up of two “techni-quarks” with “technicolor” charges. [Edited to remove confusion with Preon Theory]

It’s…an idea. But it’s never been a very popular one.

Part of the problem is that the simpler versions of technicolor have been ruled out, so theorists are having to invoke increasingly baroque models to try to make it work. But that, to some extent, is also true of supersymmetry.

A bigger problem is that technicolor is just kind of…tacky.

Technicolor doesn’t say anything deep about the way the universe works. It doesn’t propose new [types of] symmetries, and it doesn’t say anything about what happens at the very highest energies. It’s not really tied in to any of the other lines of speculation in physics, it doesn’t lead to a lot of discussion between researchers. It doesn’t require an end, a fundamental lowest level with truly fundamental particles. You could potentially keep adding new levels of technicolor, new things made up of other things made up of other things, ad infinitum.

And the fleas that bite ’em, presumably.

[Note: to clarify, technicolor theories don’t actually keep going like this, their extra particles don’t require another layer of technicolor to gain their masses. That would be an actual problem with the concept itself, not a reason it’s tacky. It’s tacky because, in a world where most physicists feel like we’ve really gotten down to the fundamental particles, adding new composite objects seems baroque and unnecessary, like adding epicycles. Fleas upon fleas as it were.]

In a word, it’s not sexy.

Does that mean it’s wrong? No, of course not. As the paper linked by Huffington Post points out, technicolor hasn’t been ruled out yet.

Does that mean I think people shouldn’t study it? Again, no. If you really find technicolor meaningful and interesting, go for it! Maybe you’ll be the kick it needs to prove itself!

But good grief, until you manage that, please don’t spread your tacky, un-sexy theory all over Facebook. A theory like technicolor should get press when it’s got a good reason, and “we haven’t been ruled out yet” is never, ever, a good reason.

[Edit: Esben on Facebook is more well-informed about technicolor than I am, and pointed out some issues with this post. Some of them are due to me conflating technicolor with another old and tacky theory, while some were places where my description was misleading. Corrections in bold.]

Physical Truths, Lost to the Ages

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For all you tumblr-ers out there (tumblr-ists? tumblr-dwellers?), 4 gravitons is now on tumblr. It’s mostly going to be links to my blog posts, with the occasional re-blog of someone else’s work if something catches my eye.

Nima Arkani-Hamed gave a public lecture at Perimeter yesterday, which I encourage you to watch if you have time, once it’s up on the Perimeter site. He also gave a technical talk earlier in the day, where he finished up by making the following (intentionally) provocative statement:

There is no direct evidence of what happened during the Big Bang that could have survived till today.

He clarified that he doesn’t just mean “evidence we can currently detect”. Rather, there’s a limit on what we can know, even with the most precise equipment possible. The details of what happened at the Big Bang (the sorts of precise details that would tell you, for example, whether it is best described by String Theory or some other picture) would get diluted as the universe expands, until today they would be so subtle and so rare that they fall below the level we could even in principle detect. We simply don’t have enough information available, no matter how good our technology gets, to detect them in a statistically significant way.

If this talk had happened last week, I could have used this in my spooky Halloween post. This is exactly the sort of thing that keeps physicists up at night: the idea that, fundamentally, there may be things we can never truly know about the universe, truths lost to the ages.

It’s not quite as dire as it sounds, though. To explain why, let me mention another great physics piece, Tom Stoppard’s Arcadia.

Despite appearances, this is in fact a great work of physics popularization.

Arcadia is a play about entropy. The play depicts two time periods, the early 19th century and the present day. In the present day a pair of scholars, Hannah and Bernard, argue about the events of the 19th century, when the house was occupied by a mathematically precocious girl named Thomasina and her tutor Septimus. Thomasina makes early discoveries about fractals and (to some extent) chaos theory, while Septimus gradually falls in love with her. In the present, the two scholars gradually get closer to the truth, going from a false theory that one of the guests at the house was killed by Lord Byron, to speculation that Septimus was the one to discover fractals, to finally getting a reasonably accurate idea of how the events of the story unfolded. Still, they never know everything, and the play emphasizes that certain details (documents burned in a fire, the true feelings of some of the people) will be forever lost to the ages.

The key point here is that, even with incomplete information, even without the ability to fully test their hypotheses and get all the details, the scholars can still make progress. They can propose accounts of what happened, accounts that have implications they can test, that might be proven wrong or right by future discoveries. Their accounts will also have implications they can’t test: lost letters, feelings never written down. But the better their account, the more it will explain, and the longer it will agree with anything new they manage to turn up.

That’s the way out of the problem Nima posed. We can’t know the truth of what happened at the Big Bang directly. But if we have a theory of physics that describes everything we can test, it’s likely to also make a prediction for what happened in the Big Bang. In science, most of the time you don’t have direct evidence. Rather, you have a successful theory, one that has succeeded under scrutiny many times in many contexts, enough that you trust it even when it goes out of the area you’re comfortable testing. That’s why physicists can make statements about what it’s like on the inside of a black hole, and it’s why it’s still good science to think about the Big Bang even if we can’t gather direct evidence about the details of how it took place.

All that said, Nima is well aware of this, and the problem still makes him uncomfortable. It makes me uncomfortable too. Saying that something is completely outside of our ability to measure, especially something as fundamental and important as the Big Bang, is not something we physicists can generally be content with. Time will tell whether there’s a way around the problem.