Electroweak theory describes electromagnetism and the weak nuclear force as one unified force. What does “unified force” mean?


If they were originally just one force, what particle carried it? Was it the photon, or was it the W and Z bosons? Did both exist, and both carried it? Then did they have different qualities, like the W/Z being massive and the photon being massless? Were they one particle that split into the photon and W/Z?

In: 4

Unified force means that both forces can be described by the same theory that is in some sense more fundamental and underlies both.

The force carriers of the electroweak force are neither the photon nor the W and Z bosons. It has four bosons of its own, called the W1, W2, W3, and B bosons (the “W”s here are not the Ws of the modern W+ and W- bosons). The modern photon, W, and Z bosons are in some sense a mixture of these bosons, in the same sense that the vector (3, 4) is in some sense a mix of the vectors (5,0) and (0,5). Similarly, the four charges of the electroweak force are different from modern electric charge and the three components of weak isospin, in the sense that electric charge and weak isospin are different sums of combinations of the four charges of the electroweak force.

The photon has different properties from the W and Z bosons because it is the name we give specifically to the part of the electroweak interaction that *doesn’t* interact with the Higgs field, which is what gives many particles (including, in particular, the W and Z bosons themselves) mass. In that sense, it’s not so much “why is the photon massless” as “why is there one dimension in this 4D space that avoids interacting with the Higgs”, because the photon is just what we call that particular thing.


It might be helpful to consider a more visualizable analogy. Suppose you’re sitting on a flat plane. It doesn’t matter what way you go: north, south, east, west, whatever, you’re going to find the same behavior. A flat plane is isotropic: it’s symmetric with respect to rotations. So you pick “north” and “east” (with “south” and “west” as “negative north” and “negative east” respectively) as your way of naming positions on your plane, but that choice is arbitrary.

These directions correspond to the bosons of a force – in some sense, for example, electromagnetism “is a circle” (which is why it only has one boson, the photon), while the strong force is a much more complex object (with three possible directions = three bosons). In this analogy they’re not physical directions – instead, they represent small changes to the states of a physical system. The flatness of the plane, and the fact that it is similar everywhere, represents a symmetry of the equations describing that system.

But now suppose you’re not on a flat plane. Instead, you’re on the surface of a cylinder. Now it *does* matter which direction you go: one direction loops back around, while the other direction runs off to infinity. The symmetry of your plane It turns out that the axis of your cylinder doesn’t run in a cardinal direction – it neither runs due north-south or due east-west. The symmetry has been **broken** – and the axis on which the cylinder lies is now a critically important parameter in the world you’re trying to describe.

So rather than continuing to use north and east as your directions, you use “lengthwise” (along the cylinder in the direction it runs off to infinity) and “circumferencewise” (around the cylinder) as your new directions, because those are a natural way to break down movement on the cylinder. Some things will be conserved lengthwise and some will be conserved circumferencewise, but often not both. So your new symmetries are movement lengthwise and movement circumferencewise, but not free movement in any direction. These new directions are *mixes* of “north” and “east”, your old choices of direction.

Similarly, since “north” and “east” represented symmetries that no longer exist, the bosons that movements in those directions are analogous to are no longer meaningful either. Instead, you have two new bosons, mixes of the old ones, corresponding to lengthwise and circumferencewise movement. And unlike the old system, where you could smoothly blend from north to east and vice-versa, now you can’t smoothly blend from lengthwise to circumferencewise – you effectively have two different things that are acting independently from one another, with no way to interconvert between them.