Coffeeshop Physics
by Jim Pivarski

We can get there from here

“Have you heard about this? Opera says neutrinos travel faster than light!”

I was in a conversation at Fermilab yesterday when I first heard about it. “Is that like one of those things where astrophysicists say that quasar jets travel faster than light, but only because they’re leaving out some projection effect?” I said.

“No, this is for real. Except— I think so. I can’t really tell; the article doesn’t say very much.”

I shrugged. I have no nose for news. It was only when my wife asked me about it that I knew it was a big story. She usually hears too much physics from me, so she doesn’t actively seek it out. By that point, it was in all the newspapers, the experimenters made their paper public, and CERN’s director general sent out a general e-mail.

If it’s true that neutrinos travel faster than light, it would be a huge upset. Some may take it to mean that relativity is overturned, Einstein rolls in his grave, and there’s no longer any limitation on the speed of future spaceships: we can get to distant stars in weeks, rather than decades. However, the implications run a lot deeper than that.

Relativity is a fact of life, as much as falling or heat and cold. We may not experience relativity in everyday things, but particle physicists encounter it daily. It’s not a small effect, something that might be a mirage. In fact, in the conversation at Fermilab I was learning about special techniques to measure particles that travel significantly slower than the speed of light: those are the oddballs. If this new observation about neutrinos is true, then it would have to fit into the constant stream of other observations. The new data would have to augment relativity— they can’t overturn it.

Relativity is about rotation. Unlike rotating a picture frame, which mixes one space dimension (the horizontal) with another (the vertical), relativity is about rotations that mix a space dimension with time. Time is a dimension very much like length, width, and height, but with a minus sign in the mathematical expressions that makes a big difference. Distances and time intervals can be measured in the same units: an inch of time is 85 picoseconds, and a minute of length is about 11 million miles. A handy unit to remember is that a foot is one nanosecond.

We can draw time and space in a single plot— I drew an example below. Looking at plots like this is a bit like viewing time on its side. Everything that has any duration, like a human life, becomes a tall, thin strand: we’re about six feet from head to foot, but three quintillion nanoseconds (95 years) from birth to death. If I drew everything on the plot, all of the streaks of stars and spaghetti of intersecting human lives, we wouldn’t be able to see anything, so I just drew one little spaceship. It enters the frame at a constant speed from the bottom, then slows to a stop at the point. The speed of the spaceship is distance-per-time: the steepness of the slope of its path. Speed is an angle.

Plot of space and time, with the path of a spaceship

Relativity is about rotations in space and time, which is to say, changing speed. Whenever you change your speed, you rotate yourself in space and time. This “mixes” space with time: you convert a little bit of what had been time into space, and what had been space into time. To explain what I mean by this mixing, below is an example of a space-space rotation. If we tilt a hanging picture, the picture’s horizontal line becomes partly horizontal and partly vertical. There’s nothing magic about that: it’s just a matter of how one defines horizontal and vertical.

Rotated picture frame

Space-time doesn’t work exactly like that, because if we rotated 180 degrees, we could reverse time! The minus sign in the mathematical expression for space-time rotations changes the picture to the one below. This is what the space-time plot would look like to someone at a different space-time angle, that is to say, a different speed.

Rotated space-time

The time and distance axes slant toward each other, and all paths squish and stretch in between. At an extreme, if we rotate toward the speed of light, the time axis and distance axis get closer and closer to overlapping. Light itself inhabits a strange world in which there is no difference between space and time.

This mixing of space and time is only noticeable at high speeds, close to the speed of light. However, there’s no boundary line: it’s always happening to some small degree. For instance, if you walk toward the Andromeda Galaxy on a Wednesday, then it becomes next Saturday in Andromeda. If you then turn and walk away from it, it becomes last Sunday in Andromeda. Your space-time angle is very small at normal walking speeds, but the axis from here to Andromeda is long enough to easily shift it by a week.

The experiment that seems to show particles moving faster than light is a collaboration between the European Laboratory CERN and the Italian Laboratory of Gran Sasso in the Alps. CERN sends a beam of neutrinos from its accelerator complex in Geneva, Switzerland to Gran Sasso’s underground (technically, under-mountain) laboratory, 450 miles away. Neutrinos pass through miles of rock without even noticing— they interact so weakly that they are effectively ghosts. In Gran Sasso, there is a large neutrino detector called Opera; the reason it is large is to improve the chances of detecting some of the few neutrino interactions. Although the main purpose of the experiment is to study the way that neutrinos of one type change into another, they also measured the time of the neutrinos’ flight and the distance between the labs very precisely in order to determine their speed. There are some alternate theories of neutrino transformation and some theories of quantum gravity that predict that the neutrinos would slow down in various ways. But instead, they observed the neutrinos traveling faster than expected, and faster than light.

There’s nothing in the theory of relativity that forbids faster-than-light particles. Their mass would be an imaginary number (i.e. mass-squared is a negative number), but that’s just strange, not forbidden. For neutrinos in particular, however, we know from previous experiments that they have non-imaginary mass differences. That would have to be reconciled somehow. If imaginary-mass particles exist, then they would never be able to go slower than the speed of light— such things were called tachyons when theorists played with the idea in string theory. The problem with faster-than-light particles is a philosophical one: they can tell us the future.

Taking the Gran Sasso measurement as a case-in-point, Gran Sasso is 2.4 million nanoseconds distant from CERN (450 miles), and they measured the neutrinos arriving 2.4 million minus 60 nanoseconds after they left CERN. These measurements were all made by stationary clocks (with the exception of a satellite, but it was calibrated for Earth-time). From our perspective, the neutrinos appear to be slightly faster than light, but from a different perspective, an observer traveling at relativistic speeds, they would be much faster than light, or even happen in the wrong order: Gran Sasso receives the neutrinos before CERN sends them. This is just what happens when you apply normal relativistic rotations to particles traveling faster than light. For an observer traveling at 99.999999992% of the speed of light, the timing of “CERN-emits” and “Gran Sasso-receives” can be completely reversed, so that “CERN-emits” happens 2.4 million minus 60 nanoseconds after “Gran Sasso-receives.” This is not an incredibly high speed: a proton with 80 TeV of energy (a little more than ten times the LHC’s design energy) would be going that fast. Faster-than-light travel is not a different thing from time-travel— if you have one, you the other.

The same event in four different points of veiw

Now imagine that the high-speed observer can emit neutrinos. As he passes by Gran Sasso, he sends neutrinos to CERN if Gran Sasso received neutrinos from CERN. If CERN gets neutrinos, they choose not to send neutrinos to Gran Sasso. Now neutrinos only get sent around if they don’t get sent around: a paradox!

Box-diagram of the paradox

If this faster-than-light thing stands up to scrutiny, you know this is the first thing we’ll try to do. You just know it is.

So what about that measurement? Can we believe it? There’s a strong temptation to pull something out of the procedure and say, “This part must be wrong; the whole thing is crap,” but after reading their paper and listening to the spokesperson’s presentation and response to questions, I don’t see any obvious faults. They took it very seriously and measured nearly all steps in the chain multiple times in multiple ways. There’s another strong temptation to say, “Gee wiz, time travel!” but that would be jumping way ahead of the facts. It takes time to confirm an observation, to find the same thing emerge in so many different ways that it must be true. I want to believe it or disbelieve it: I hate suspense! The hardest part of science is the ache of uncertainty.

The first caveat in the experiment is that the initial time of each neutrino is not known. When I heard about this experiment, I imagined someone starting a clock at the instant that the neutrino was produced at CERN and someone stopping a clock when it was received in Gran Sasso. Not quite. In order to make large batches of neutrinos (in the hopes that a few will be seen), they are produced in long bursts from the accelerator, about 10 thousand nanoseconds from start to finish. The neutrino that is detected in Gran Sasso might be from the start of the burst, the end of the burst, or anywhere in between. How, then, could they have possibly measured a 60 nanosecond difference in arrival time?

They accumulated a large number of neutrinos (16 thousand) and statistically fitted the distribution. CERN measured the shape of the burst, the Opera detector cataloged the arrival times of all the neutrinos, and the analysis team varied the time-offset between the shape and the observed distribution until they fit. Here’s what that looks like (copied from their paper):

Fitted distribution of neutrino events

The start-time of any one neutrino is unknown, but you can learn what you need to from a distribution of all of them. This is standard practice in particle physics, especially where the uncertainties of quantum mechanics play a role. It looks like a good fit, but the relevant scale is 60 nanoseconds, while the horizontal axis covers 10 thousand nanoseconds. They provide a close-up of the leading and trailing edges, which are the most important parts of the fit:

Close-up of the leading and trailing edges

The other caveat about the measurement is that it could not be performed by a single clock. There must be at least two clocks: one at CERN and the other at Gran Sasso, and they need to be synchronized. But the experiment is in a hard-to-reach location, so a long series of clocks is needed, including a satellite link. Even something as mundane as cabling could ruin the measurement: electronics signals pass through cables close to the speed of light, which is 60 nanoseconds = 60 extra feet of cables. The electronics themselves needed to be carefully calibrated, since signals pass more slowly through computers than wires. The distance also had to be surveyed through all the tunnels that lead down to the underground experiment. The surveying operation was complicated by the fact that they could only close one lane of traffic.

The only way to know if there isn’t an error somewhere in the chain is to cross-check each step carefully. I got the impression from the spokesperson that a lot of different techniques were used to do all of this double-checking, and there were naturally a lot of questions about each part. The number of reviewers has just increased dramatically, but we need to wait to see if someone finds something.

Even though I can’t say that I know the result is wrong, I have a strong suspicion that neutrinos do not travel faster than light. My personal bias is based on the philosophical paradox that would be raised if anything could travel faster than light.

Suppose that closer investigation reveals some error, or that follow-up experiments do not find any faster-than-light neutrinos. This sort of thing has happened before. Would that be a disappointment? I bet most of the excitement over this result is the expectation that it would make a Star Trek future possible: it’s a bummer that stars are so far away, especially the ones with the most interesting aliens. I mean it. Many science fiction universes have some kind of faster-than-light travel for good reason.

But this isn’t necessary. Relativity, the cursed limitation on our space-faring dreams, provides its own escape. While a spacecraft cannot reach a star 20 light-years away in less than 20 years, as measured on Earth, the crew of the spacecraft would enjoy a shorter trip. This is especially true if the spacecraft were accelerating all the way there.

Suppose that a spacecraft accelerates toward its destination at a rate equal to Earth’s gravity: 9.8 meters per seconds-squared is equal to 1.0 light years per years-squared. The craft gradually becomes relativistic during the first half of the trip, turns around half way and slows down during the second half of the trip. The relationship between traveler time and Earth time is exponential: light years take years, but millions of light years take decades. These are all the places we could go:

(light years)
traveller time
Proxima Centaurithe closest star4.23.5
Epsilon Eridanithe closest exosoloar planet (unconfirmed)10.44.9
the Gliese 581 systeman exosoloar planet that may be habitable20.36.07
the Pleiadesthe Seven Sisters40011.7
Gemingathe nearest known pulsar81513.1
Crab nebulait’s beautiful6,50017.1
the supermassive black hole at the center of our galaxyare you kidding?25,00019.7
the nearby supernova that exploded in 1987to see the rings168,00023.42
the Andromeda Galaxythe nearest (big) galaxy2.6 million28.7
the Sombrero Galaxyit looks like a hat!29.3 million33.4
Cygnus Athe nearest known quasar600 million39.3

We can get there from here— we can go anywhere in the universe in a lifetime. But we can never come back.