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It's All Relative
by Michael Kelsey

Einstein's Big Idea homepage

E = mc2 is probably the most recognized physics equation among the general public, beating out Newton's Second Law of motion, F = ma. Despite that recognition by the outside world, E = mc2 is hardly ever used all by itself by practicing physicists for any sort of calculation. It is only true if you are talking about masses that are at rest. The total energy of an object includes both the "intrinsic energy" of the mass itself as well as the extra energy coming from the object's motion. In particle physics, nothing we study is ever at rest, and so E = mc2 on its own doesn't really help us to solve problems.

Einstein's most famous equation is really an icon, a symbol for the whole fabric of special relativity that Einstein discovered and laid out for us to use in 1905. That fabric is the core both of our understanding of the nature of matter and of how we produce, manipulate, and analyze the tiny, short-lived bits of matter that lead us down the road of that understanding. Relativistic quantum mechanics, my specialty, focuses on conservation of energy, conservation of momentum, and how particles interact with one another and transform from one kind to another while keeping all mass and energy balanced. Without all of that, none of my work would make sense or even be possible.

My own physics involves colliding high-energy beams of electrons and positrons (antimatter electrons) to produce new, short-lived particles. Those particles decay into groups of two or three (or more) other short-lived particles, which decay in turn, until we end up with a spray of a few to a dozen or more particles stable enough to pass all the way through our three-meter-thick collection of detectors. At every step of that process, relativity is essential to making our devices work correctly and to understanding the data that come out.

Creating collisions

We accelerate electrons using electric fields inside copper pipes. Microwaves help generate and maintain these fields. If the electrons were made to "go faster" by that acceleration, then at each step of the process they would cover a longer and longer distance in each time step, and we would have to continuously change the microwave frequency to match. But relativity tells us that the speed of light is a maximum limit. The more energy we put into accelerating our electrons, the closer their speed gets to c, but no matter how much energy we put into them, they can never move faster than c. The benefit of this to us is that we can design our system as though the electrons have constant speed, and hence we can use the same microwave frequency everywhere. The electrons get more and more energetic, but relativity means that they pass through each section of pipe in the same amount of time.

I can’t imagine my work without E = mc2.

The equivalence of mass and energy explained by E = mc2 is what allows us to create the anti-electrons we use in our collisions. After accelerating the electron beam, we take a part of that beam and aim it into a stack of heavy metal (tungsten) plates. As the electrons pass close to the metal atoms, some of the energy of their motion transforms into mass, into pairs of new electrons and positrons, moving forward along with the initial beam at high energy. Those new particles in turn have some of their energy turned into additional electron-positron pairs, and so on. After many such interactions, much of the beam's energy has been converted to mass. What comes out the far side of the stack of plates is a "spray" of electrons, positrons, and gamma radiation (photons). We use complex magnetic fields to capture and collect the positrons, and then we put them through the same accelerator to get them up to high energies.

In a similar way, when we collide our beams of electrons and positrons head on, the energy they carry, including the energy of their own mass, transforms to produce new particles (called "B mesons"), which fly away from each other. The initial particles are extremely massive—together the two of them add up to almost the total energy available from the beams. The little bit of energy that didn't transmute into mass is left for getting the two B's moving in opposite directions. We use the equations of relativity and quantum mechanics to carefully adjust the energies of the electron and positron beams so that they are just enough to produce the massive particles we are interested in studying.

Decoding decay

When a B meson decays, special relativity (and quantum mechanics) govern how the resulting products move. I mentioned above that E = mc2 only applies to things that are at rest. The full expression is really

E2 = (pc)2 + (mc2)2

where p represents momentum, the product of mass and velocity. Energy and momentum conservation tell us that the motion of things before the decay, and the motion of things after the decay, have to add up to be equal. From all of this, if we measure the momenta and identify the types (masses) of the final particles from the decay, we can work backward to determine the mass, momentum, and energy of the original B's.

The B's are normally produced moving in opposite directions at about six percent the speed of light. At that speed, they would travel only about 28 microns before decaying. One goal of our experiment is to measure properties of B mesons with respect to the time before they decay, but 28 microns is too short a distance to reconstruct or measure reliably. We take advantage of another aspect of Einstein's relativity, time dilation, to "stretch" the particle's lifetime as we see it. Our electron and positron beams have different energies, which means that all the particles created in the collision and decay are moving together relative to our detector, at about half the speed of light. This motion stretches the B lifetime, as we observe it, so that they travel about 250 microns—about 1/100th of an inch—before they decay. This is large enough for us to measure reliably by reconstructing the trajectories of the decay products.

In short, the mathematics and physical reality of Einstein's relativity suffuse every aspect of the particle physics experiments I do every day, from the production of the beams we collide, to the analysis of the data that comes out of the detector. I can't imagine my work without E = mc2.

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For Michael Kelsey, the essence of special relativity is everywhere in experimental particle physics.

BaBar 1

This chamber of the BaBar particle detector that Kelsey works with uses over 10,000 phototubes to provide precision views of the faint light that particles produce as they travel through its particle identification system.

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Einstein's Big Idea

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Michael Kelsey is an experimental particle physicist working with the BaBar particle detector at the Stanford Linear Accelerator Center in California. The goal of BaBar is to explain why there is more matter than antimatter in the universe. It works to detect B mesons and their antimatter equivalents, anti-B mesons, which result from collisions of electrons and positrons traveling at nearly the speed of light.

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