Little Knobs on the Control Panel of the Universe

How do forces work on the quantum scale?

Noone can truly picture how quantum particles interact via quantum forces, so we’re limited to analogies. The following is an analogy that I think exposes some of the key features. Consider the asteroid belt that lies between Mars and Jupiter…

Quantum forces and the asteroid belt

The only way they can interact (one rock affecting the trajectory of another) is by exchanging momentum via collisions

Image one of these rocks breaking apart into two. Due to conservation of momentum, they move in opposite directions. Perhaps one is a lot larger than the other, so we can loosely think of the bigger one as the continuing story of the original rock (call it Rock A), and the smaller one as a bit of shed skin. The emission of the little rock causes the rock A to be deflected slightly in the opposite direction.

The little rock may then collide with another, call it rock B, and stick to it, be absorbed by it, this will cause its host’s movement to be deflected a little. The overall result is; rocks A and B have been deflected in the opposite direction to each other. If your telescope was strong enough to see rocks A and B but not the messenger that travelled between them, it would look almost as if there was some repulsive force pushing them apart. It’s not a mysterious invisible influence like gravity pushing them apart, it was due to an exchange of a thing that carried momentum between them. Such a thing one could call a force carrier.

The italicised words above are all borrowed from particle physics. The electric repulsion of two electrons is because they are exchanging force carriers in a similar way to the asteroids. In this case the force carrier the beloved photon, the particle responsible for the electric force. This is the way all fundamental forces work (except maybe Gravity, no one knows shit about Gravity), the exchange of force-carrying particles.

Less intuitive and connected to the asteroids is the case where a force is attractive. Try to imagine the little messenger rock carrying “negative momentum” and when it hits rock B, it pulls it towards the direction it came from instead of away. I never said the analogy was perfect.

asteroids.jpg    coarseasteroids.jpgFig.1: asteroids exchanging a rock, causing an effective repulsion between them. Left- close up, right- from afar.

The strength of a force

Consider again the asteroid belt. Could we work out, on average, how much of an influence rocks have on each other? In other words, what is the strength of the force between them? The property of the rocks one should look at is their crumbliness, the propensity for them to shed little rocks, and accept little rocks to stick to them.

In analogy, the strength of the electric force should be proportional to the probability at any point in time that an electron will emit, or absorb, a photon. Then, the total probability of two electrons “interacting” via a photon, would be proportional to the probability of photon emission from electron A, times that of the photon being absorbed by electron B.

Could we put a number on this fundamental property of the electron? There are nuances to this question, but loosely speaking, I can give you a number. It is roughly 1:137. Consider any electron in the universe, and you can rest assured there is always a 1 in 137 chance that it is emitting or absorbing a photon (this is modulo the complicated relationship between probabilities, quantum mechanical amplitudes, phase spaces, other caveat sources I haven’t thought of, and factors of π).

As a fraction, it’s expressed as α = 1/137, this is called the fine structure constant. It quantifies the strength of the electric force. (Actually, it dictates the strength of both the electric and magnetic forces, since they’re essentially two sides of the same coin. From now on I’ll refer to as the electromagnetic force).


Fig.2: Probability of an electron emitting a photon = α = 1/137

If α was different, the energy shells in atoms would go haywire, chemistry would change at its core, the frequency of light coming from stars would shift, and change α too much, electrons could escape the atom altogether. The value of α has a strong bearing on the world around us.

Imagine God, or some cosmic architect, had created reality and was responsible for maintaining it, so had to sit in a control room full of levers and switches and the like. α would be the label under one of the little knobs on the control panel of the universe.

There are other little knobs required to control the other forces of nature. For example the strong nuclear force binds the building blocks of the nucleus (quarks) together. It has a strength which is proportional to the probability of a quark emitting or absorbing a gluon, the corresponding force carrier. This probability is called αs, and is much bigger than α, with a value close to 1. Hence it’s name, it’s hella strong compared to the electromagnetic force.

Fiddling with the knobs

Imagine what could happen if you could reach out and turn one of these knobs, changing the fundamental parameters of the universe. The results would be something reserved for our wildest imaginations. Right?

In fact, this has happened in the history of the universe.

The fundamental parameters have changed on the cosmological time scale. In the past, not so long after the big bang, α was much larger than it is today, and αs was much smaller. Atoms could not form, as the strong nuclear force couldn’t live up to its name. The universe was a different place that followed different rules. We don’t know much about this chapter of cosmic history, but we know it was hot, energetic, and chaotic, certainly with no sensible “structures” like stars, planets, or asteroid belts.

The universe has “phases” in the same way H20 does. At different temperatures, H20 exists as vapour, water or ice. Water freezing into ice is referred to as a phase transition; when the macroscopic nature of the substance changes.

Over time the universe has cooled from this rather unimaginable plasma into what we know today, via (probably) many phase transitions. For example, there must have been a transitional period when αs became strong enough to pull previously free quarks together and bound them into nuclei.

A Grand Unified Knob

While I’m rolling with this analogy, there’s one last thing that is defo worth a mention. Physics today has managed to describe three (of a total four) fundamental forces of nature using this picture of force carriers and all that. Electromagnetism, the strong nuclear force, and the weak nuclear force. There are three corresponding numbers which quantify their relative strengths, α, αs we’ve already mentioned, and a third that controls the weak nuclear force that I’ll call αw.

All three varied throughout the age of the universe. We understand reasonably well how each varied. In the past αs was weaker, and α, αw were stronger. We can extrapolate the behaviour of these three numbers into the past using what we know about the forces and how they interact. Something special happens to the three numbers if we go all the way back to 0.0000000000000000000000000000000000001 seconds after the big bang.

At this time, all three numbers head towards the same single value. All the forces were the same strength. There is no a priori reason to expect this to happen, on the face of it it seems like a total accident. But physicists tend to think this is too special an outcome to be an accident. There must be something deeper afoot.

It’s led the particle theory community to ponder if all three of the forces originate from a single force, governed by what is called a grand unified theory, boiling down to a single number that controls it all. Perhaps the control panel is in fact a single dial that just says ‘universe’ on it. No direct evidence of such a theory has been found yet, but such evidence may be waiting just around the corner.

FullSizeRender (1).jpg

Fig.3: Strength of forces throughout the history of the universe.

More about force carriers

α, αs, and αw

Why do the strengths of forces change?

Could the strength of forces vary through space as well?

Grand unified theories


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