String Theory

You may have read about physicists proposing that everything is made of vibrating strings. It’s hard to get an intuitive grasp of this concept, but perhaps the following will help get you started.

Light can be thought of as a particle or a wave, depending on what experiment you do to detect it. If you look to see how it exposes a photographic plate or hits a screen, you discover that light particles, photons, have one-to-one collisions with molecules and land in a specific place on the screen (rather than wash across a screen like a wave washes up on a beach.) If you check to see how light passes through tiny holes you see interference patterns, places where light waves cancelled and reinforced.

It turns out that all particles (not just light) have a wave nature. For example, electrons travel through slits and produce interference patterns. You’ve heard of the electron microscope, which uses electrons rather than light to view tiny objects. The electron’s wavelength is smaller than that of visible light, so we can us electron waves to detect smaller objects.

Three formulas, two formulas from Einstein, and one from de Broglie, are helpful here. The first is Einstein’s famous E=mc2, which tells how much energy is needed to create a particle of mass m, or how much energy will appear if a particle of mass m vanishes. (c is the speed of light.) The second, also from Einstein, is E = hc/λ, where λ is the wavelength of the wave associated with that particle. This gives the energy of a particle with a given wavelength.

The third formula is λ = h/mv, where λ is a particle’s wavelength, h is a constant, m is the particle’s mass and v is its velocity.

String theory? Here goes.

First, get the idea of strings made of atoms out of your mind. Forget what they are made of and just consider them to be imaginary. Here’s how they work, in a nutshell.

Consider a tiny particle, like an electron, proton, muon, whatever. The particle has a mass. When moving, it has a wavelength (equation 3) and an energy (equation 2). Now picture two girls turning a skipping rope. They are making a standing wave. Their shoulders are nodes, hardly moving. Most of the energy of the wave is near the centre of the rope where the amplitude is greatest. Picture a particle to be equivalent to a standing wave: the “probable location” of the particle is where the energy is greatest. But the particle does not actually exist in a spot, its energy (and mass, equation 1) are spread out all the way between the nodes.

If the girls wiggle their arms differently, they could set up a standing wave with two loops and a stationary point, a node, in the middle. (You never actually see this when kids are skipping, but you can do it with your stretched-out phone cord if you try. Turn it at twice the rate of the “skipping rope” turning.) In this case there are two high-energy locations, the loops or antinodes. This wave is the first overtone of the original, which is called the fundamental. Buglers (and all brass instrumentalists) make use of the overtones to get different notes without changing their fingers. (Buglers can’t change their fingers: they have no valves!)

Now the intuitive step. What if the overtone represents a different particle from the original? That is, since every particle has a wave nature, we could think of particles as different resonances of a vibrating string, different frequencies where standing waves can be set up. The more massive the particle, the more energy (equation 1). The more energy, the smaller the wavelength (equation 2). The more massive particle could be a standing wave of higher frequency or an overtone of the wave associated with the less massive particle.

String theory is much more complicated than this, of course. But the idea here is to turn on a little light bulb in our brain, a little spark of intuition. Because of the wave-particle duality of light and matter, perhaps we can think of particles as resonances of strings. It is space itself which is resonating, not actual pieces of thin rope.

To test out the theory we can use some symmetry considerations to predict a resonance that no one has seen before. This leads to a frequency and wavelength prediction. That gives an equivalent mass and velocity (equation 3). When we let high speed particles race down linear accelerators and smash into atomic targets, tiny particles are produced. They don’t last long, and when they vanish, they give off a burst of light. The photon will have an energy equivalent to that particle’s mass (equation 1). This energy has an associated wavelength (equation 2) which translates to a colour. So, when we fire up our linear accelerators, synchrotrons, and cyclotrons (“atom smashers”) we can look for a burst of light of that colour. If we see it, we can say that we have discovered a new particle and announce its mass.

Alternatively, if we have a tiny understanding of string theory, we can say we have witnessed a new resonance of one of the strings of which the universe is made.