If you watch just about any video about fundamental physics, you’ll be told that
there are four known fundamental forces: gravity, electromagnetism,
and two nuclear forces. You’ll even be told how strong they are. What if I told you that
those videos only tell you part of the story? Sounds like it’s time to do a deeper dive.
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In books and articles about frontier physics, it’s entirely common to be told
of four fundamental forces. Gravity was the first to be understood and it keeps
us firmly on the ground and guides the planets through the heavens.
Electromagnetism is a blend of electricity and magnetism, first really understood in the 1800s,
but it also explains how light works, as well as playing a key role in chemistry.
The strong nuclear force is the one that holds protons and neutrons together in the nucleus of
atoms. Without the strong nuclear force, the only element out there would be hydrogen.
And, of course, there is also the weak nuclear force, which is frequently mentioned as being
responsible for some radioactivity. I made a video that explains why that’s only part of the
story. The link is in the description below. When authors and video creators list the forces,
they order them in terms of how strong they are. The usual list says that the strongest
of the forces is the strong force. If you call the strength of the strong force to be the basic unit,
we can say that it has strength of one. Then, each in turn, we say that the strength
of electromagnetism is about point zero one, the weak force is about ten to the minus fifth power,
and gravity is a paltry ten to the minus forty power.
And that’s the story we tell. Of course, if you think about it for the tiniest moment, you realize
that this simple statement is utter hogwash, or at least an incomplete telling of the tale.
After all, you’ve lived your entire life and unless you’re a physicist, you’ve never
encountered the strong nuclear force and you have plenty of experience with gravity. Your day-to-day
experience tells you that gravity is way more important than the strong nuclear force.
So, what’s the deal? What it boils down is that the different forces have different behaviors.
The way that the strength of the forces change with distance isn’t the same.
To illustrate the idea, suppose there were two hypothetical forces, one that is very strong
for close distances, but gets weaker for long distances, while there is a second force that
is weaker at short distances, but doesn’t change. In this situation, one force is stronger than the
other at short distances, while the other is stronger at long distances. You can’t say which
one is stronger without more information. For the list of strengths I mentioned earlier,
the distance that was chosen is about ten to the minus fifteenth meters, or a femtometer.
That’s about the size of a proton, which is, of course, super, super small. But
it’s the size at which particle physics experiments are done, so it makes sense.
Let’s talk about each force in turn. Let’s start with electromagnetism and gravity,
because both of those forces act the same way. They both weaken as the square of the distance
between two objects. Double the distance, and the force goes down by four. Triple the
distance, and it goes down by nine. If you’ve heard about Coulomb’s law,
which describes the behavior of electric forces, and Newton’s law of gravity, which handles,
of course, gravity, you can do this yourself. Now there are some subtleties here. The k variable
in the Coulomb equation sets the strength of the electromagnetic force, while the G
term sets the strength of gravity. But both of those depend on the units – the unit of electric
charge in the case of electromagnetism and mass in the case of gravity.
We can see what that means by looking at the ratio of the force of gravity and electromagnetism
between two identical particles. We take the two equations, take the ratio, and we find that the
ratio between gravity and electromagnetism doesn’t depend on distance. It’s the same everywhere.
What matters is the charge to mass ratio. And this isn’t a constant. For example,
take the electron and the proton. They have the same amount of charge, but different mass.
So, for two electrons, gravity is 4.2 times ten to the forty-two power times weaker,
but for two protons, gravity is only 1.2 times ten to the thirty-six times weaker.
The second is nearly three and a half million times bigger than the first.
And that’s how one compares gravity and electromagnetism. The strong force is different,
for example, its strength has a very different dependence on distance.
If two objects that are capable of experiencing the strong force are very close to one another,
they feel very little force between them. However, when they get about a femtometer apart- which
is about the size of a proton- the force gets stronger rising to about ten thousand newtons,
or a bit over a ton for my American viewers. The weird thing is that the force doesn’t change
as the particles get farther apart. It’s basically constant. But, like when you stretch a rubber
band, the energy does increase. Once the two particles are separated by a distance of several
times the size of a proton, there’s so much energy stored, that the energy converts into matter,
making new particles. These new particles arrange themselves so the original particles
no longer feel any force between them. So, for the strong force, for very short
distances, the force is zero. For biggish distances, the force is also zero. But for
the distance range of about the size of a proton to a few protons, the force is super strong.
Okay- that’s gravity, electromagnetism, and the strong nuclear force. What
about the weak nuclear force? Well here, other factors matter.
A different factor comes into play. At the quantum level, forces are created
by force carrying particles jumping between two matter particles. That’s known to be true for
electromagnetism and the strong and weak forces, and it’s thought to be true for gravity.
For electromagnetism, gravity, and the strong force, the force carrying particle is massless.
But for the weak force, those force carrying particles are heavy – very heavy. Each one
weighs nearly a hundred times as much as a proton, which is approaching a hundred billion electron
volts. And that changes everything. In fact, for most nuclear decays,
the energies involved are about a one million electron volts. Don’t sweat the units,
just remember that most radioactive decay involves one and, in those units, the weak force particles
would weigh in at about a hundred thousand. Since the energy of nuclear decay is way too small
to make a weak force particle, you’d think that weak force interactions wouldn’t occur. However,
quantum mechanics comes into play here. While the mass of weak force particles are, on
average, about a hundred thousand, those particles actually have a range of masses. You can see the
range here. Where the curve is high, lots of those particles exist. Where the curve is low, very few
do. And we see that while the number that exist down at one are very small, they’re not zero.
However, the farther from normal they are, the shorter amount of time they can exist.
This is a straight up consequence of the Heisenberg Uncertainty Principle,
which says that the lifetime of a thing, which is delta T, times the distance in energy from normal,
which is Delta E, has to be greater than this constant, called the reduced Planck constant,
or hbar, divided by two. If you put in the numbers, you
find that the weak force carrying particles can only exist for a very short time. In fact, they
can only live long enough to travel no longer than a distance about 1/1000 the size of a proton.
So this tells us something. The weak force is weak because it’s rare. Two objects have to be
closer than 1/1000 the size of the proton for the weak force to come into play in nuclear physics
interactions. Below that size, the weak force is relatively strong. And it’s all because of
the mass of the force carrying particles of the weak force. If this big mass wasn’t a factor,
the weak force and the electromagnetic force are pretty similar in strength.
One final topic I want to mention is the decay of top quarks. Top quarks are the heaviest
known subatomic particle. They decay 100% of the time into bottom quarks and a weak force
particle. That’s just what they do. As it happens, it takes about ten to
the minus twenty three seconds for the strong force to have time to come into play. However,
the top quark decays in the staggeringly short five times ten to the minus twenty five seconds,
or about five percent the time it takes for the strong force to do something.
This means that in the case of the decay of the top quark, the weak force happens faster
than the strong force. So weak is strong and strong is weak… or something like that.
So, what’s going on? It’s because the mass of the top quark is ginormous – it’s more
than twice as big as the mass of the weak force particle involved
in the decay. So the huge mass of the weak force particle isn’t an obstacle at all.
It’s like someone wanting to spend five hundred dollars. If you’re a poor college student,
five hundred bucks is an entire month’s food budget…maybe more. So, spending it
is a big deal. On the other hand, if you’re a multi-millionaire, you can drop that kind of
money on a single bottle of 2002 Cristal. So, what’s the bottom line? The bottom line
is that the simple hierarchy of forces you learn about in popular science books and many
videos- including mine- are just the tip of the iceberg. It’s not enough to know how the forces
act at a particular distance and energy. A deeper understanding means that you need to understand
how they behave under a variety of conditions. And, once you fall into that rabbit hole,
you find that it’s a long way down.
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Okay- that was a much deeper dive into
some of the behavior of forces than you get in most popular science treatments. Even this video
only scratches the surface. What did you think? Do you want more deep dives? Or should we broaden the
subject matter we cover? Let us know your thoughts in the comments and we’ll take them into account
as we talk about future programming choices. And, of course, we hope you’ll subscribe to
the channel. The more the merrier. As we build our viewership, you’ll encounter more people who think
like we do- good people- you know… the kind of people who realize that physics is everything.
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