Knocking on Heaven's Door - Lisa Randall [51]
We need to be more clever—or more ruthless, depending on how you look at it, to detect what is happening on the tiny scale of a nucleus. Small wavelengths are required. That shouldn’t be so hard to believe. Imagine a fictional wave with wavelength equal to the size of the universe. No interaction of this wave could possibly have sufficient information to locate anything in space. Unless there are smaller oscillations in this wave that can resolve structure in the universe, we would have no way, with only this enormous wavelength wave as our guide, to determine that anything is in any particular place. It would be like covering a pile of stuff with a net and asking where your wallet is located in the mess underneath. You can’t find it unless you have enough resolution to look inside on smaller scales.
With waves, you need peaks and troughs with the right spacing—variations on the scale of whatever it is we are trying to resolve—to be able to identify where something is or what its size or shape might be. You can think of a wavelength the size of the net. If all I know is that something is inside it, I can say with certainty only that something is within a region whose size is that of the net with which I caught it. To say anything more requires either a smaller net or some other way of searching for variations on a more sensitive scale.
Quantum mechanics tells us that waves characterize the probability of finding a particle in any given location. Those waves might be waves associated with light. Or they might be the waves that quantum mechanics tells us are secretly carried by any individual particle. The wavelength of those waves tells us the possible resolution one can hope to attain when we use a particle or radiation to probe small distances.
Quantum mechanics also tells us that short wavelengths require high energies. That’s because it relates frequencies to energies, and the waves with the highest frequencies and shortest wavelengths carry the most energy. Quantum mechanics thereby connects high energies and short distances, telling us that only experiments operating at high energies can probe into the inner workings of matter. That is the fundamental reason we need machines that accelerate particles to high energy if we want to probe matter’s fundamental core.
Quantum mechanical wave relations tell us that high energies allow us to probe tiny distances and the interactions that occur there. Only with higher energies, and hence shorter wavelengths, can we study these smaller sizes. The quantum mechanical uncertainty relation that tells us small distances connect to large momenta combined with connections among energy, mass, and momenta provided by special relativity make these connections precise.
On top of that, Einstein taught us that energy and mass are interconvertible. When particles collide, their mass can turn into energy. So at higher energies, heavier matter can be produced, since E = mc2. This equation means that larger energy—E—permits the creation of heavier particles with bigger mass—m. And that energy is ecumenical—capable of creating any type of particle that is kinematically accessible (which is to say light enough).
This tells us that the higher energies we currently explore are taking us to smaller sizes, and the particles that get created are our key to understanding the fundamental laws of physics that apply at these scales. Any new high-energy particles and interactions that emerge at short distances hold the clues to decoding the underpinnings of the so-called Standard Model of particle physics, which describes our current understanding of matter’s most basic elements and their interactions. We’ll now consider a few key Standard Model discoveries, and the methods we now use to advance our knowledge some more.
THE DISCOVERIES OF ELECTRONS AND QUARKS
Each of the destinations on our initial tour of the atom—the electrons circulating around