Lecture 16

Matter and Anti-Matter

The families of quarks and leptons we have introduced are replicated in another set, the anti-particle families. Each fundamental quark or lepton can exist in two forms, either the "matter" form we are familiar with, or a corresponding "antimatter" form. Particles and anti-particles are essentially identical to each other (in mass, lifetime, type of interactions they are affected by, etc.), but are opposite in electric charge, as well as in any other charge the particle might possess (apart from the more familiar electric charge, particles also carry "strong" charges, "weak" charges, etc.).

The first indication of the existence of the anti-world came with the discovery, in cosmic rays experiments in the 30's, of a particle identical in all respects to the electron, but with a positive charge. Even though a surprise, the existence of such particle had been predicted by theory. As the study of elementary particles proceeded, it was confirmed that for every existing particle its anti-counterpart does exist. While it is a fact that our universe is made of positive protons and negative electrons, an antimatter universe (or star or galaxy), made of positive electrons and negative protons is perfectly plausible.

On the other side, we have no evidence whatsoever of any sizeable conglomeration of antimatter in the universe, and this strong matter-antimatter asymmetry is one of the questions facing modern cosmology.

The most striking facet of the matter-antimatter properties is that, if a particle encounters it own anti-particle, the two can completely annihilate their mass and disappear in a puff of pure energy, i.e. photons. Notice that the annihilation into pure energy is not the only possible outcome of particle- antiparticle encounter: an electron and positron pair of high enough energy could for instance transform themselves into a proton and an antiproton, or any other particle-antiparticle pair.

Science and Science Fiction

The intriguing potential for annihilation has, since the discovery of antimatter and its properties, fueled the imagination of science fiction writers. As a recent example, Star Trek's Enterprise spaceship is equipped with an antimatter engine. While undoubtedly large scale energy generation by means of matter anti-matter annihilation would represent the most copious and efficient source of energy, and is theoretically possible, it still belongs to science fiction for the following reasons :

1.

the basic antimatter "fuel" is not available. Even though we can "create" tiny amounts of antimatter in high energy accelerators, this process is extremely inefficient, and, to create an anti-particle we need to provide much more energy than what we could recover from its annihilation

2.

even if we were to improve our techniques, or find an "antimatter deposit" somewhere in outer space (a very unlikely prospect), we do not know how to contain it in a "fuel tank" and prevent it from annihilating its container....

On the other side, a practical, and rather impressive, application of antimatter does exist in the medical field, in the form of the PET (Positron Emission Tomography) scan.

The fact that antimatter is not so exotic after all, is proven by the existence of isotopes that undergo a type of $\beta$-decay somewhat different from the one we have encountered. In certain nuclei, it is possible for a proton to decay according to

$p\rightarrow n e^{+} \nu$

(this reaction is rigorously forbidden for a free proton because of energy/mass conservation). When crossing ordinary matter, the positron emitted in such a process will soon annihilate with an atomic electron, generating two energetic photons (i.e.$\gamma$ rays). The photons energy will have to balance the initial positron energy, plus the mass of the electron/positron pair, about 1 MeV. Such energetic photons are easily detected.

In the medical application, small quantities of a positron emitting isotope are injected into the patient, and the progress or accumulation of the isotope-carrying substance throughout the body is monitored by detecting the emitted $\gamma$ rays.

The Fundamental Forces and their Carriers

We are all familiar with Gravitational Forces and we are all well aware of Electromagnetic Forces too. By studying the nucleus and its interior, we have also learnt of the existence of two short range forces that become relevant only at the level of subatomic scales, the Strong and Weak Nuclear Forces.

To the extent of our knowledge, these are all the forces that exist in nature and control its behaviour : leaving aside theological considerations, we can say that any event that takes place (or that could or will take place) in the universe is the effect of one or more of these forces !!

Let us examine some of the characteristics of these forces. To start, we know that two of them (gravity and electricity) have infinite range, while the other two are not felt beyond distances larger than nuclear or subnuclear dimensions.

We also know that not all objects are affected by all forces : neutral bodies are not affected by the electric force, leptons are not affected by the strong force, etc. In Newton's classical theory of gravitation, only objects with mass are affected by gravity, but Einstein's General Relativity theory showed that the gravitational pull extends also to massless objects (e.g. light).

Next, we can compare the relative strength of the four forces: if we were to assign the strong force an arbitrary strength value of 1, the others are in the ratio:

strong : EM : weak : gravity = 1 : 10^-2 : 10^-5 : 10^-39

It might be of a surprise to you to find out how incredibly weak the gravitational force is !! If gravity is so weak, how can we explain that its effects are the most visible in our everyday's experience? The reason is twofold:

1.

gravity has an infinite range

2.

there is nothing that can cancel the force of gravity. Unlike electricity, where positive and negative charges cancel each other, our experience has shown that there is only "positive" gravity. In a massive body like, for instance, the sun, the gravitational pull of each individual molecule adds up to produce an extremely large force.

Force as an Exchange, and Force Unification.

When trying to understand the nature of forces, for a long time scientists (and, in the old days, philosophers) have wondered how two objects can exert a force on each other even when they are far apart. Nowadays, we feel that we have a good explanation for this "action at a distance", since we believe that a force is the manifestation of a particle exchange between the objects at play.

There is a standard example that gives a good intuitive idea of how the exchange of an object can generate the equivalent of a repulsive force. Imagine a skater, initially at rest, throwing an object to another skater. Upon the throw, the first skater will recoil and start moving in a direction opposite to the object's trajectory. When the second skater catches the object, he will also start moving away from the first skater.

If they keep throwing the object to each other, it is as if a force is acting to push them apart. It is not at all intuitive how the exchange of an object can also generate an attractive force, but this is what does happen at the quantum level.

The current description of the fundamental forces states that to each force corresponds a well defined particle, responsible for being the force carrier, i.e. for transmitting the force among different objects. What are these particles? The most familiar one is the carrier of the electromagnetic force, the photon. The repulsive force felt by two charged particles of the same sign (e.g. two electrons) is caused by the exchange of photons (= electromagnetic radiation) between them. The energy of the exchanged photons will determine the strength of the interaction. It is an immediate consequence of the theory that, if the force has an infinite range, then the carrier must be massless.

In a similar way, it is believed that gravitational interactions are "mediated" by the exchange of a massless particle called graviton. Due to the extreme smallness of the gravitational force, gravitons have not yet been detected, but an active research program is underway to detect gravitational waves (i.e. gravitons) produced by stellar collapses.

The strong and weak forces have their own carriers. The carrier of the strong force was named gluon, this is the particle that, effectively, provides the glue that holds the nuclei together. The discovery of the carriers of the weak force was one of the greatest success stories of modern particle physics.

Predicted to exist as very massive particles by the theory of the weak interactions, they were experimentally produced in high energy collisions between protons and antiprotons, and were found to have exactly the properties predicted by the theory.

The discovery of the carriers of the weak force was extremely important, since it confirmed another prediction of the theory, i.e. that, as strange as it might sound, weak and electromagnetic forces are just two aspects of a unique underlying more fundamental interaction. The unification of the weak and electromagnetic force represented a major step in the continuing attempt find the simplest possible description of the physical world.

In the history of physics, we have witnessed a few very important unifications: Newton showed that the falling of objects on Earth and the motion of planets in the sky were just two aspects of the same universal gravitation. Maxwell's equations, in the past century, provided the complete connection between electricity and magnetism, showing that they are two manifestations of a unique entity. The confirmation of the correctness of the "electroweak" hypothesis has been another major step towards a more unified view of the universe. There are good reasons to believe that, eventually, all the four known forces will be shown to have a common origin and nature. This quest for Grand Unification is one of the major goals of forefront research.

Relativity

We live in a tri-dimensional word. If we want to fully specify the position of an object we can choose arbitrarily a set of three orthogonal axes, and define the position, and the variations of position, of the object by giving its coordinates with respect to the three axes. If we also want to specify the time at which the object has a given set of coordinates, then we should attach a clock to our axes: this is what we call a reference frame. It should be obvious that we can choose the reference frame any way we like it. In fact we can describe the motion of an object either in a frame which is at rest with respect to it, or from the point of view of a frame attached to it.

Probably the first scientist to discuss how the appearances of motion depend upon the frame of reference was Galileo, who made the following example :
suppose that a sailor, sitting high up in the mast of a moving ship, drops an object (Galileo loved to drop objects, from the leaning tower of Pisa, from a ship's mast, etc...). The object will fall down along the mast, and drop at its base : from the point of view of the sailor, the object has fallen in a straight vertical trajectory. But, from the point of view of an observer on land, the ship was moving therefore, as the object fell to the bottom of the mast, it followed some sort of curved trajectory. Who is right? Obviously they both are, but the conclusion that we reach is that space trajectories are not absolute quantities, but are relative to the frame of reference in which they are observed.

Similar considerations can be made for velocities: suppose you are playing table tennis, the ball goes back and forth at velocities of about one meter per second. If now you were having the same game on board of a plane, moving at 400 miles per hour (about 180 m/s), the ball would appear to you to move at the same velocity as if on the ground, but for a ground based observer it is moving at 180 plus or minus a few meters per second : like displacements, also velocities are relative to the frame of reference. This is what is called Galileian relativity.

In spite of these discrepancies, nobody would doubt that the physical laws are independent of the frame of reference (otherwise, given the abitrarity of the frame's choice , we could not even define physical laws!). Moreover, we would all believe that, in spite of the differences in the observations, the times measured by our clocks would always be the same, regardless of the motion of the frame they are in. As we will see, while the first assumption is correct, the second one will need to be revised....

Einstein, in addition to being one of the greatest minds of all times, was also somewhat of a (peaceful) revolutionary and had a very independent mind. This free spirit prevented him from getting a good conventional University job at the end of his studies, so that he had to content himself with employment in the Swiss Patent Office. Still, this might have been a bonus, since it gave him the time and the freedom to think of whatever problem he cared.

And the main problem that was intriguing him was a big discrepancy between the standard laws of motion, and Galileian relativity, versus the basic laws of ElectroMagnetism, an extremely successful theory summarized by Maxwell's equations.

According to Maxwell's equations, electromagnetic radiation must propagate at the speed of light (hence the inference that light is a form of electromagnetic radiation), and this result is obtained regardless of the state of motion of the light source. How can this be reconciled with our expectation that, like any other motion, the speed of light, as seen by an observer at rest, should depend on the motion of the object emitting light?

This, and other considerations, led Einstein to formulate his revolutionary, but almost necessary, hypothesis :

Light, and any other electromagnetic radiation, always moves at the same speed c, regardless of the motion of the observer and/or of the light source.

It is remarkable how, just this very simple, albeit very daring, hypothesis, together with the constraint that laws of physics must be the same regardless of the frame of reference, are practically all that is needed to build the revolutionary Theory of Relativity.

As we will see, one of the most surprising consequences is that, like displacements and velocities, also time is not an absolute quantity, but it does depend on the frame of reference.