Beyond the God Particle (18 page)

Figure 5.11. Cosmic Sequence of Light Events.
Light emanates further into the universe from the firecracker event. At any given time, t (we call it a “time slice”), the radius of the sphere of photons is given by (radius) = c t.

MOTION IN SPACE-TIME

We can use space-time diagrams to represent things that happen in any physical process. For example, we can use a space-time diagram to represent the motion of particles. Light is made of photons that always move at the speed of light. We can trigger the emission of photons by an event at which a flashbulb goes off. Photons then propagate outward in all directions at the speed of light. In space-time the photons are seen to move forward in time at ever-increasing distances from the flashbulb. This traces out a cone in space-time, what we call the “light-cone,” spreading out in space and time from the point at which the photons were initially produced.

Figure 5.12.
The motion of two photons is indicated by the arrows. These individual photon paths lie on the “light-cone,” emanating into the future from an event that emitted them at the origin. Photons always travel at the speed of light, c.

By comparison, a single massive particle, like a muon, can in principle travel at any speed, up to nearly the speed of light. A muon, because it has mass, can also sit still. These possibilities are shown in
figure 5.13
. A muon at rest simply moves, like we all do, forward in time with no progression in space. On the other hand, a very fast muon is one that moves forward in time but also progresses outward in space in some direction.

Figure 5.13. Motion of Muons.
A muon can have arbitrary velocities less than the speed of light. (a) shows a muon nearly at rest that “moves” forward in time but not in space. (b) shows a faster muon. (c) is an ultra-fast muon traveling at nearly the speed of light.

We can make a muon move very, very fast, but we can never get any massive particle to travel at exactly the speed of light. At the LHC, protons are made to travel at 99.999999 percent of the speed of light. The muon's
little sister, the electrons at CERN's LEP synchrotron, were made to travel 99.9999999925 percent of the speed of light. And we have very sensible ideas about someday building a Muon Collider in which we would get muons to travel at 99.99999999 percent the speed of light. But never will an electron or a proton or a muon get to 100 percent of the speed of light. Nature has an ultimate speed limit that is the speed of light. And the existence of mass implies, according to Einstein, that it would take an infinite amount of energy to make any massive particle travel at the speed we call “c.”

But suppose, somehow, we could do a master experiment: make a muon have zero mass. We don't know how to do that exactly, but we could get very, very close to this situation experimentally, by making the muon travel as close to the speed of light as possible relative to us. The closer we get the muon to the speed of light, the more and more the muon behaves, as we observe it in our lab, like a massless particle. We can do this with our very powerful future Muon Collider, and as the speed of the muon approaches c, the effects of its mass become undetectable to us. So, what happens to a very, very fast muon as it starts to act like a massless particle?

MUON AT THE SPEED OF LIGHT

From a distance we see a small single-prop airplane flying through the air—it appears to be moving in straight and true line on this clear, sunny day. But what about its propeller? The propeller is moving along the same straight line, but the tips of the propeller are executing a corkscrew-like motion. This is how any spinning object—in this case, the propeller—moves through space and time when it is also in uniform motion.

Recall that the muon has spin. We can never stop a muon from spinning. The spin of a muon is always “up” or “down” along any axis. So we find, upon very careful observation, that a muon (or an electron or a quark) traveling at a high speed moves through space-time like a propeller. The muon, like a corkscrew entering a wine bottle cork, or a drill bit drilling into wood, spins either clockwise or counterclockwise as it progresses through space. This is the “up” or “down” binary nature of the muon's spin combined with motion.

But time is frozen as the muon approaches the speed of light. How can it spin if time is frozen? The way to think of this is that the muon's path through space-time is like that of a corkscrew, either corkscrewing to
the right or to the left. The two different corkscrewing paths are the two quantum states of spin, “up” or “down.” As the muon approaches the speed of light, these two quantum states become completely independent of one another—the muon has become schizophrenic—it has split into two different personalities altogether as it approaches the speed of light!

This splitting in two of the muon is the consequence of effectively turning off the mass of the muon by approaching the speed of light and by freezing time. The mass of the muon blends the two personalities into one, the usual muon that is heavy and at rest in our lab. But without mass, the muon always travels at the speed of light and then becomes one of two separate and different and independent entities, either a clockwise or counterclockwise rotating corkscrew, or propeller, or drill bit, or whatever metaphor you fancy—it's just one of two different possible massless muons.

If at this point you are starting to feel a bit uneasy, that somehow the elegant simplicity of mass as a mere “quantity of matter” is about to be lost forever, then we suggest that you open a fine bottle of Pinot Noir with a corkscrew wine bottle opener. Now, of course, your bottle opener will turn in one particular way as it penetrates downward into the cork in only one direction. My corkscrew turns clockwise as it descends deeper into the cork.

We have to be precise about what we mean by “clockwise”; that is, we define “clockwise” by looking down from above along the shaft of the corkscrew to the top of the wine bottle. And you can withdraw the corkscrew from the cork by turning it the other way (counterclockwise). And that is an important feature of a drill or a corkscrew—it will rotate one way as it goes in one direction, and the opposite way when it goes the opposite direction! As you contemplate a fresh glass of Pinot Noir, try to figure out if your corkscrew rotates clockwise or counterclockwise as it goes into the cork. To our knowledge, for no particular reason, all corkscrews are manufactured to turn clockwise (looking down from above) as they go into the cork. But there's no reason in principle why there cannot exist a counterclockwise rotating corkscrew. It's just a question of how they were fabricated. Call up the factory and order a dozen counterclockwise corkscrews. Maybe some corkscrews are counterclockwise, while most are clockwise—we're not sure. So, if there are clockwise and counterclockwise corkscrews, these are independent objects like the two pieces of the muon that become separate and independent when we turn off the muon's mass.

CHIRALITY

There's a fancier and more sophisticated way to describe this. We'll assume that you are right-handed (this is unfair to you southpaws, but it is just the way things are defined, so please accept our apology). As you rotate the “clockwise” corkscrew with your right hand by curling your fingers around the knob or handle on the corkscrew, in the manner shown in
figure 5.14
, you will see that the progression of the screw into the cork is pointed in the direction of your thumb. This is also true for most wood screws or metal screws when you are tightening them with a screwdriver. It's called the “right-hand rule.” The right-hand rule states that “the direction of progression of (most) screws is the direction of your thumb as you rotate the screwdriver by curling your fingers of your right hand around the handle.”

Figure 5.14. Corkscrew.
A right-handed corkscrew will progress into the cork in the direction of the thumb of the right hand as the fingers curl around the handle of the screw.

For any rotational motion that is also accompanied by a linear progression, we say the system has “chirality.” Our corkscrew in the above example has “right-handed chirality,” and we'll call it chirality “R.” But, as we said, we can always manufacture a corkscrew that advances into the cork as we rotate counterclockwise. The progression into the bottle as we turn the handle with our left hand would then point in the direction of the
left-hand thumb. This is a corkscrew with the opposite chirality, a “left-handed chirality” corkscrew, and we'll call it chirality “L.” Likewise, we can have an ordinary wood screw that is “left-handed” and requires rotating the screwdriver in the opposite way to drive the screw into a block of wood.

THE SPACE-TIME PICTURE WITH CHIRALITY

The approximately massless muon, traveling at almost the speed of light progresses through space as much as it is progressing through time, either with chirality L or chirality R.

So now we can depict our massless muon as it travels at the speed of light. It is either a right-handed, R, or a left-handed, L, particle. If the spin of a particle is pointed along the eastern direction as it moves east, then it is R; and if the spin is still pointing east but the particle is moving west, it is L. The R muon state is completely independent of the L state of the muon—the muon has essentially broken apart into two distinct particles, L and R.

Of course, this ambidextrous L and R quality of very fast particles like high-energy muons comes from the quantum phenomenon of spin. But the two spin states of the
resting
or slowly moving muon are easily related: we can simply rotate the muon and one spin (e.g., “up”) flips into the other (“down”). And, the
resting muon has no chirality
—it is sitting still, so there is no “progression through space” associated with the spin. But, as the muon travels near at the speed of light, we cannot rotate one chirality state into another anymore (we would have to stop the muon to do this). For a muon traveling east, the two spin states of the muon that were “up” or “down” have now become “spin pointing east” (R chirality) and “spin pointing west” (L chirality) and are now two independent particles. Note that chirality, L or R, is the
combination of the direction of the motion and the direction of the spin
. Chirality involves both of these concepts, linear motion and spin, combined together at the same time.