Irregular Webcomic! #3272

Not actually the remains of my car, thankfully.

I was driving this week, when another car hit me from behind. Nobody was injured, thankfully, but the young driver in the car behind was understandably in a state of mildly shocked agitation about the incident. I suspect my car came off the worst, as the rear hatchback door is now jammed solidly shut despite all my attempts to open it. Fortunately I didn't have a week's worth of groceries in there. (Don't worry, that's not my car in the photo above or on the side.)

Cars are designed these days to crumple on impact. It wasn't always like that. Cars used to be designed to be as solid and strong as possible. At first thought, that makes sense. You don't want you car to be crushed like a paper bag when it hits something, as that obviously isn't safe, so going to the opposite extreme and making it as hard and rigid as possible seems appealing. Until you look at the physics of what happens in a collision.

There are two physical quantities that are conserved in any interaction of matter. The first is energy, which we've talked about a fair bit already. In a collision between, say, two cars, the kinetic energy of the cars moving at their pre-collision speeds is converted into other forms of energy. The cars may still be moving immediately after the collision, so some of the kinetic energy remains as kinetic energy, but much is lost as heat and, most noticeably, sound. Some of the energy is "used up" in doing the work necessary to deform the body panels of the cars. This energy goes into breaking some of the chemical bonds that give structural integrity to the panels. Or pieces of plastic and glass as well if you're particularly unlucky.

The second quantity that is preserved is momentum, which I've talked about before too. Momentum is the product of mass and velocity, and has a direction. So if two cars of equal mass and speed collide head-on, the total momentum before is actually zero, since the directions cancel. After the collision, the momentum of the stationary pile of metal is also zero. The energy, however, has gone from huge to zero, and the release of all that energy is what causes the damage.

Accelerating a car down a road. Creative Commons Attribution image by Nikos Koutoulas.

To bring the speeds of the colliding cars down from something large to zero or something close to it, they need to accelerate. Common usage of the word "accelerate" is to mean when something goes faster, but in physics terms acceleration is simply a change in velocity, whether that change be faster or slower, positive or negative.^[1] In the case of a crash the acceleration is decidedly negative.

Crashing cars tend to go from a high speed to a low speed within a very short space of time. This means a very high acceleration, because acceleration is equal to the change in velocity divided by the time it takes the change to occur.^[2] If a car is travelling at 60 km/h and brakes normally, it can come to a stop in about 3 seconds. The acceleration is 60/3 = 20 km/h per second. If the same car hits an oncoming car and stops in half a second, the acceleration is 60/0.5 = 120 km/h/s.

And here's where things get dangerous. The parts inside a car and the human body can only withstand so much acceleration. If you slow down at 20 km/h/s, that's normal; you do that in traffic every day. If you slow down at 40 km/h/s, that's like slamming the brakes on hard to avoid a collision. You get jerked against your seatbelt. If you slow down at 120 km/h/s, you get slammed violently against the seatbelt, the steering wheel, the dashboard, the windscreen, and possibly the road if you weren't wearing a seatbelt. Modern cars have inflatable airbags to absorb some of this impact between your body and bits of the car, but it's still not exactly what you'd call safe.

The easy way to generate flint sparks is with a lighter. Creative Commons Attribution-Share Alike image by Chris Isherwood.

So the other thing modern cars have is a body that crumples. The old solid car bodies, which seemed like a good idea at the time, were very rigid. This meant that in a collision they came to a stop really quickly, because there was nothing else for them to do. A solid block hitting an obstruction just has to stop as quickly as possible, because there's no flexibility, or give, or squishiness. The impact is over in a very short time. But we realised it's better if the car is a bit squishy. A squishy block hitting an obstruction can squish a bit. This spreads the collision out over a greater length of time. The result, as explained above, is that the acceleration needed to stop the car is substantially lower than if the car was more solidly built. So the effect on human passengers is less severe and less dangerous. In effect, we've decided to sacrifice the car to save our lives. That's a trade off I'd make any day.

Collisions of course don't just occur between cars. They happen when things fall and hit the ground, when animals fight or attack one another, when waves smash against rocks, and when objects in space crash into one another. One type of collision led to a major technological breakthrough in human history: the collision of flint with steel.

Flint is a very hard stone composed of very small crystals of quartz. Steel is a refined form of iron, with a controlled amount of carbon impurity to make it harder than pure iron. Despite this, flint is harder still, and when a piece of flint strikes a piece of iron, the collision scratches off small particle of iron. If done forcefully enough, the energy of the collision goes into heating up the flakes of iron to a point where the burn, combining rapidly with oxygen from the air to form iron oxide (commonly known as rust). These burning flakes of iron form sparks, and if one strikes a suitable inflammable substance such as dry tinder, it can set it alight, and so begin a fire. If the sparks strike somethign more volatile, like black powder, they can set off an explosive reaction that can fire a bullet - this is how flintlock guns work.

The Crab Nebula pulsar imaged by NASA's Chandra satellite. A significant source of cosmic rays impacting Earth. Public domain image from Wikimedia Commons.

Another interesting type of collision that we don't think about in day-to-day life is the collision of cosmic rays with the Earth. Cosmic rays are highly energetic subatomic particles and gamma rays that travel through interstellar and intergalactic space. The particles are mostly single protons and alpha particles (remember an alpha particle is the nucleus of a helium atom, composed of two protons and two neutrons bound together by the strong nuclear force). There are also a few heavier particles, which are the nuclei of atoms like lithium or beryllium, and even a tiny bit of antimatter in the form of antiprotons and positrons (the antiparticle of the electron). These particles are all travelling through space at close to the speed of light. (The gamma rays, of course, being electromagnetic radiation, travel at the speed of light.)

Now if these particles and gamma rays collided with your body, you'd be in a similar amount of trouble as if you were in a car crash, though the problem would be very different in nature. Because when a high-energy particle or gamma ray hits animal tissue, it dumps all of its energy into the tissue, which rips the electrons off many of the atoms there by overcoming the electron binding energy. This disrupts chemical bonds, breaking down important substances like the proteins and fats that make up your body. If you get exposed to enough radiation, the raw damage to your tissue can be enough to make you sick or even kill you. But even worse, a much smaller dose can damage the DNA and other structures inside your cells (which I discussed here). If this happens, your cells can "lose their programming". The instructions encoded in the DNA for making proteins may be corrupted, or the ribosomes and enzymes may be corrupted, resulting in the cell being unable to make the chemicals necessary to grow and function properly. Worse, the cell may begin making things your body doesn't need. If such a damaged cell can still manage to divide and multiply, this leads to the disease we know as cancer.

Fortunately for us, we live not on the very outside of Earth, but buried roughly 100 km inside its atmosphere. The atmosphere protects us by intercepting almost all of the cosmic rays. What's actually occurring are innumerable collisions. An incoming cosmic ray will usually hit a molecule of the Earth's atmosphere somewhere between 50 and 100 kilometres above sea level. Some make it lower, but the atmosphere rapidly gets thicker, and by the time sea level is reached there are very few incoming cosmic rays left.

Cosmic ray air shower simulation. Creative Commons Attribution image by Dinoj Surendran and COSMUS Group, University of Chicago.

But the collision with a molecule of air is not the end of the story. Because the cosmic ray carries a large amount of energy, it has to go somewhere. What it ends up doing is generating more subatomic particles, converting the energy to mass according to Einstein's E = mc² formula. The total mass-energy after the collision is the same as before, so these new particles have lower kinetic energy, meaning they're moving more slowly. These secondary cosmic particles then collide with further air molecules, and some of them can also generate further particles that move more slowly still - though the speeds are still a considerable fraction of the speed of light. Furthermore, some of the particles generated are unstable and rapidly decay into yet other particles, generating more particles at each step. This process continues in a chain reaction known as a cosmic ray air shower, as the particles multiply and spread out a bit like the water spray from a bathroom shower-head.

Some of the particles produced in these air showers can reach the ground. The most common are neutrinos, which are not a problem because they barely interact with matter at all. Cosmic shower neutrinos generally pass right through people, the ground, and in fact right through the Earth and out the other side, without causing any further damage whatsoever. There are millions passing through your body right now as you read this.

The next most common are muons, which are from the same particle family as the electron and so have similar properties, but are approximately 200 times heavier. These are actually unstable too, and decay with an average lifetime of about 2 microseconds - but this is long enough for some of them to reach the ground at the very high speeds they are travelling when generated by the air shower.^[3] These muons can be detected using sensitive instruments, which we use to measure cosmic ray showers. By measuring multiple muons with different detectors at the same time, we can triangulate and determine that they came from the same position high in the atmosphere, thus giving us a way to measure the altitude of the initial cosmic ray collision with the air.

ATLAS detector at the Large Hadron Collider. Creative Commons Attribution-NonCommercial-No Derivatives image by Simon Bisson.

The generation of cosmic ray air showers is related to another useful form of collision. In the past decades, we have built several large machines specifically to cause collisions. The most famous one recently is the Large Hadron Collider, but there are also many other smaller particle colliders around the world. The goal of such machines is, essentially, to recreate reactions akin to very high energy cosmic ray collisions in the lab. More precisely, the various particle colliders smash together specific subatomic particles at speeds very close to the speed of light.

The reason we have needed to build successively larger (and more expensive) machines to do this is because we want to extend our knowledge of subatomic particle physics to particles of heavier and heavier masses. The only way we know to generate such particles is to make use of Einstein's relation, and provide enough energy in a small enough space that some is converted to mass in the form of the particles we wish to study. And the only way to do that is by more and more energetic subatomic collisions.

Before 2012, one of the greatest successes of this branch of experimental physics was the discovery and confirmation of the W and Z bosons. These were particles predicted in 1968 during the formulation of the theory which provided a combined explanation for electromagnetism and the weak nuclear force, proposed by Sheldon Glashow, Steven Weinberg, and Abdus Salam.

Their theory explained these forces very elegantly, but only if they included a set of new fundamental particles, then unknown. They called them the W and Z bosons. (There are two W bosons, one each with positive and negative electric charge, and one Z boson, with no electric charge.) The problem was that the boson—or particle which "carries" the force—related to electromagnetism was already well known: it is the photon. The W and Z bosons should also have been evident in experiments performed up to that time, if they had no mass like the photon. The problem could only be solved if they posited that the W and Z bosons had mass. This led Peter Higgs to propose a mechanism for why these bosons had mass. Besides explaining why the W and Z bosons were not massless, the so-called Higgs mechanism also predicted the existence of a further particle, called the Higgs boson.

Thankfully these collisions don't produce particle showers. Notice the crumpling of both vehicles to absorb energy. Creative Commons Attribution-NonCommercial-Share Alike image by Eva Ekeblad.

Anyway, out of all this theory came numerical predictions for the masses of the W and Z bosons, assuming the theory was correct. The predicted mass for the W bosons was 80.39 giga-electron-volts (GeV), and the Z boson 91.187 GeV. (For comparison, a proton has a mass of 0.938 GeV.) The problem was that in the 1960s there were no particle accelerators big enough to produce collisions with enough energy to produce W and Z bosons of the predicted masses. This changed in 1981 when the Super Proton Synchrotron came online in the CERN research facility in Switzerland. This collider could reach the energies needed, and in 1983 two separate experiments led by Carlo Rubbia and Simon van der Meer first detected and then confirmed the particles as products of the collisions. They measured the masses and found the W bosons were 80.39 GeV and the Z boson was 91.188 GeV, with experimental uncertainties very small, but large enough to encompass the predictions made nearly 20 years earlier. This was a stunning example of how science can make predictions that later become tests of the theory. In this case, the theory passed with flying colours.

Fast forward to 2012, and the Large Hadron Collider. The major missing piece of our model of particle physics was the Higgs boson. The problem was its predicted mass: at least 125 GeV - substantially bigger than the W and Z bosons. The LHC was built specifically to try to confirm the existence of the Higgs boson. The collisions it produces are the most concentrated bursts of energy we are capable of producing. If we could find the Higgs boson, it would be the final validation of our understanding of the physics of fundamental particles. If it could not be found, then it would be an indication that there is a problem with the theory. As it turned out, two teams working independently at the LHC found strong evidence of a new particle with a mass of 125 GeV, which displays all the expected characteristics of the Higgs boson in terms of electric charge, spin, and how it decays into smaller particles.

As with all science, this is not enough to prove the newly detected particle is the Higgs boson, and there are still some tests that are planned to rule out other possibilities. But for now the CERN scientists are confident there is indeed a 125 GeV particle, and that there is no evidence that it is not the Higgs boson. As they carry out further experiments over the next few years, our confidence will grow (or be shattered as something contradictory comes to light!). Either way, we will learn something wonderful and new about how our universe works.

And all because of collisions.

Title image is Creative Commons Attribution by Damnsoft 09 at en.wikipedia.

[1] Or even sideways or at some other angle. A car moving at a constant speed but turning is accelerating sideways.

[2] Strictly speaking, this is the average acceleration over that period of time. The instantaneous acceleration at any point of time within that period may be different, and is defined in terms of the "rate of change" of speed, which generally requires a bit of calculus to figure out. It's exactly analogous to the concept of average speed versus instantaneous speed: If you travel 10 km across the city in your car and it takes you 20 minutes, that's an average speed of 30 km/h, but at any given time your instantaneous speed (or your rate of change of distance travelled) could be 60 km/h as you move freely along a road, or zero, when stopped at a traffic light, or any value in between or slightly higher.

[3] Observant readers will notice that even moving at the speed of light (c), 2 microseconds is only enough time to travel about 600 metres. However, remember that objects travelling at speeds close to light experience time dilation. The measured speed of cosmic-ray-generated muons at the Earth's surface is from 0.994c to 0.998c. At 0.998c, a muon experiences time flowing approximately 16 times more slowly relative to an observer on Earth, so the muon can travel an average of almost 10 kilometres before decaying. And that's an average - some travel further than this.