8 The impact of special relativity
In this course, we have looked at the effect of Einstein’s postulates upon classical mechanics. However, special relativity had a wider ranging impact. In this coda, we will look briefly at its impact on other areas of physics.
8.1 Electromagnetism
In a sense, the impact of special relativity on electromagnetism was limited, since Maxwell’s laws were already compatible with Lorentz transformations. Essentially, special relativity indicated that it was electromagnetism that was correct and our understanding of space, time and classical mechanics that needed fixing.
However, special relativity allows us a better understanding of electromagnetism. It explains how an effect that appears, to one observer, to be due to an electric field might appear to be due to a magnetic field to a second observer. Moreover, scalar and vector quantities in electromagnetism can be unified into 4-vectors (or tensors). For example, the electric scalar potential and the magnetic vector potential form the components of the electromagnetic 4-potential, while charge and current density may also be unified to form the 4-current. The unification of the electric and magnetic fields is more complicated, as these are combined to form a tensor — the electromagnetic field tensor.
8.2 Gravity
The effect of relativity on the theory of gravity was much more significant. Newton’s theory of gravity requires action at a distance — if the sun were to mysteriously disappear then this would immediately affect the motion of the Earth. Yet transmission of information faster than the speed of light is forbidden1. Einstein’s solution was to adjust his postulates so that the principle of relativity holds for free-falling frames, rather than inertial frames. This small-seeming modification then leads to the curvature of spacetime2 and the possibility of black holes and gravity waves!
1 In special relativity, this would cause problems with causality, e.g. the possibility of sending messages into one’s own past.
2 Curved spacetimes naturally require more sophisticated mathematics than you have seen in this course. Indeed the very notion of a vector or a 4-vector will need to be rethought, though general relativity makes heavy use of the 4-vector notation that you have just seen.
8.3 Quantum mechanics
Quantum mechanics was in its infancy when, in 1905, Albert Einstein published his work on special relativity. It would be another 20 years before Ernst Schrödinger published his equation. Yet Schrödinger’s equation for the time evolution of a particle is not Lorentz invariant. Much effort was expended in trying to find a Lorentz invariant equation that would successfully model the evolution of particles within quantum mechanics, with limited success.
Eventually this direct approach was abandoned and students are now taught (in our fourth year) the quantum theory of fields. Happily, when quantising fields, particle-like fluctuations emerge from the theory, to explain the fundamental particles that we see3.
3 It is ironic that the fundamentals of particle physics does not deal with particles at all, but with fields.
Naturally, a knowledge of special relativity is essential for studying the quantum field theory that underpins particle physics and the understanding the mechanics of the collisions that happen at the Large Hadron Collider.
8.4 The way we think
Finally, special relativity and the developments that followed have fundamentally altered the way in which we think about space and time. Previously, space and time were considered fixed and understood — the stage upon which physics is performed. Special relativity revealed that we did not understand this stage as well as we had previously thought. General relativity would later reveal that this stage is more complicated still and is, moreover, not fixed, but affected by what takes place upon it.