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.
(intro music) 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. (phasing sound) 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. (outro music)
