Tuesday, April 10, 2007

Physics Q&A #2: The Fundamental Forces (part 1)

Welcome back to Physics Q&A, where I answer physics questions sent in by readers in order to help give you all an understanding of how the universe works. This week I'll be addressing the fundamental forces of nature, explaining how they work and how they differ.

First, let me just give you a brief overview of the forces, before we get into the details of how they work:

Acts on: Everything that has either mass or energy
Effect: Weak attraction between objects with mass or energy

Electromagnetic Force
Acts on: All charged particles and light
Effect: Attractive force between objects of opposite charge, repulsive force between objects of same charge. Acceleration caused by and/or causes light waves. Effects of special relativity give rise to magnetic effects between moving charged particles.

Weak Nuclear Force
Acts on: Leptons, quarks, and neutrinos
Effect: A bit complicated. Basically, the trick here is that all Weak interactions change the form of the particles involved. As such, it's really not a good idea to characterize this as a force, but more as an "interaction." Some people extend this to all the fundamental "forces."

Strong Nuclear Force
Acts on: Quarks
Effect: Binds quarks together to form baryons, or binds baryons together to form nuclei.

That's the essentials of it. If you want to get into the nitty-gritty of how they work, head below the fold.


Let's start out with the oddball force: Gravity. As far as modern physics can tell, gravity acts in no way like the other forces. While the other three fit well under a model of interchanging particles (called "Gauge bosons"), Gravity fits best under the model of General Relativity.

So, at this point, you're likely wondering exactly how this model works and how it differs from Newtonian gravity. Of course, the actual equations aren't simple, but I can still explain it in qualitative terms.

The key realization that gravity worked differently than other forces was the fact that a particle's acceleration due to gravity was independant of its own mass. This then tied in with a law of mechanics you may or may not have heard: The path an object takes when under the influence of no outside forces is independant of its property. But, does this mean that the converse (If an object's path is independant of its properties, it's under the influence of no outside forces) must be true?

Logically, it doesn't have to be, but it's something at least worth investigating, and that's what Einstein did, leading to his formulation for General Relativity. In doing this, he realized that, for instance, a person standing on a surface in a gravitational field would feel a normal force pushing out from the surface that would be exactly the same as a person outside a gravitational field would feel if that surface were being accelerated upwards. This formed what is known as the Equivalence Principle - that a gravitational field is equivalent to an "acceleration" of space.

So, he set up equations as if an object in freefall (a path independant of its properties) were in a natural path, and holding it out against gravity were unnatural. This led to the formulation of what's known as the Schwarzschild metric, the fundamental equation of GR. (If you've forgotten what a metric is, I recommend you check my last Physics Q&A post.)

That's the history of it, but what does it all mean? In essence, the presence of any type of energy warps space such that the natural path of objects through time now curves towards it. You can picture this as matter sitting on a giant rubber sheet, with "time" pulling downwards. Objects like Earth then warp the sheet around them:

Someone standing on the surface of Earth also feels time pulling them downwards, but now they also see that space under them is slanted towards the center of Earth. This means that if their path goes that way, they'll get ahead in time faster, so they're also pulled inwards. Now, this isn't exactly how it works, but it's good for visualization.

The Electromagnetic Force

Let's proceed onto the simplest of the three forces that can be explained from the Particle Physics model: Electromagnetism. I'll just be focusing on the electric side of it for this post, as it's all that's actually needed for the fundamental model (magnetism is just the interaction of it with special relativity).

First, the basics of it: Objects have one type of charge, which can be either positive or negative. Objects with the same sign of this charge feel a repulsive force between each other, objects with the opposite sign of this charge are attracted to each other. The force of this repulsion or attraction is proportional to the magnitude of each charge and the inverse-square of the distance between the particles to a first-order approximation.

On very small scales, electromagnetism works through what's pictured as an exchange of particles (in this case, photons). To picture this, imagine you and a friend are standing on a sheet of ice. You have a heavy ball, and you throw it over to your friend. As you release it, conservation of momentum pushes you back. Then, as your friend catches it, conservation of momentum pushes them away from you as well.

That works for the repulsive case, though the attractive case is a bit more difficult. For this case, you have to imagine that the ball you're throwing has negative mass. This way, when you throw it out, it's momentum is like it's going backwards, so you're pulled forwards too. And when your friend catches it, they get pulled closer to you as well.

Since this is the simplest case, I'll take this chance to introduce you to Feynman diagrams, which are what we use to chart this exchange of particles. In these diagrams, we start out by writing out the initial particles at the bottom and the final particles at the top. For instance, if it's an interaction between two electrons, this step would look like:

Then, we draw some possible connection between the beginning and end. In this case, the simplest is simply each of the electrons at the beginning making a straight path to one of the end ones, but this represents no interaction between them, so it's not very interesting. If we want to do some actual interactions, we need to first define what type of vertices are allowed. For EM interactions, there's only one basic type of vertex: Some charged particle comes in, emits or absorbs a photon, then goes out:

A few notes on the lines:

  • Straight, solid lines represent massive particles (such as electrons)
  • Other types of lines represent gauge bosons. For instance, photons are represented by squiggly lines as seen above.
  • The arrow on the line represents the direction of travel of a normal particle. If it points in a direction opposite that of the momentum of the particle, this is considered to be the corresponding anti-particle.
We don't need to worry about the last point for this interaction, since no antiparticles are involved. So, using this type of vertex, we end up getting two possible interactions that only include two vertices:

Once we go through a ton of complicated math using these two interactions, we can come with equations to govern it. However, it turns out that there are also a ton of possibilities (infinitely many) that use more than two vertices, but they're much less likely to occur. In the end, you get an infinite series of interactions which you can sum up, and the convergence is how things will end up behaving in the real world.

One of the big strengths of this manner of handling physics is that it doesn't only govern forces between two unchanging particles. For instance, we can also use it to represent an electron and a positron annihilating each other. To do this, we use the last point of my explanation of what the lines mean above. This way, we could make a reaction where an electron and a positron come together and turn into a photon. However, we run into a problem with this reaction in that it turns out to be impossible for momentum to be conserved. It is possible to conserve it, though, in a somewhat more complicated reaction that produces two photons:

But wait! If we can't conserve momentum for a single vertex, how come we can use that vertex within the chart? The trick here is that the internal lines we're using don't represent actual particles - there's no point in time you could freeze the interaction and see an intermediate electron. These are what we call "virtual" particles. They never actually exist in real space, but travel through imaginary space to help mediate the reaction. As such, they don't have to obey standard equations of motion, so they're allowed to have imaginary momentum or negative energy and other crazy stuff.

Now, I'm getting the feeling that a lot of you likely aren't completely following at this point, so before I continue on to finish up with the even more complicated forces, I'm going to stop the post here and open it up to questions.


Bronze Dog said...

I think you got electromagnetism's attraction/repulsion reversed.

Infophile said...

Fixed, thanks for pointing that out.