Dazzling Numbers
Researchers at the Relativistic Heavy Ion Collider have recently been able penetrate some of the mystics of the beginning of our universe. They collide the nuclei of atomic particles to simmulate the conditions of the first few microseconds of our universe. These collisions generate extremely hot, dense bursts of matter and energy. By pumping the collisions they try to discover new particles and thus verify and improve the theoretical models of the laws of physics. The values of the pressure, density, size and time of these collisions are so inmense that we cannot imagine their meanings anymore. In this article I try to make the numbers more imaginable by using analogies and metaphors.
I was reading an article about particle physics in the Scientific American. The article really was about the behaviour of quarks and gluons in very high collision energies. Physicists try to define which particle are created when colliding gold nuclei with almost the speed of light. I will not bother you with the exact details of the physics involved. Mainly because I don’t understand them myself.
When reading the article I came across lots of numbers of temperatures, pressures, speeds etc. These numbers really dazzled me. When I see a very large number I always try to find an analogy to understand the number. I mean, how big really is 1012? I know it’s a trillion, but what does that mean? In this article I will try find analogies for the numbers in the SA article.
The Relativistic Heavy Ion Collider (RHIC) on Long Island is used to smash heavy atoms into each other (or their nuclei to be exact). When doing this two large rings which are 3.8 km wide packed with magnetic coils are pushing the nuclei to ever higher speeds. When the nuclei have reached a speed of 99.99% of the speed of light (300.000 km/s) they will cross the two beams and let the nuclei crash into each other. This collision creates very high energies and with that all kinds of exotic particles are created. The temperature of the particle cloud is around 5 trillion degrees Celsius. The pressure reached during the collision is 1030 times the atmospheric pressure. The time that the particles exist is around 5×10-23 sec. The distance between the particles (quarks) needs to be smaller than 10-13 centimeter to make the strong nuclear force small enough to let the quarks break free.
So let’s see if we can understand these numbers. First the speed. 99.99% of the lightspeed (299.792.458 m/s) means that it will travel around the world 7.49 times each second. Within the 3.8 km ring it will pass through it’s starting point 78.885 times per second.
The temperature reached is 5 trillion (5×1012) degrees. Water melts at 0 degrees and boils at 100 degrees. Iron melts at 1510 degrees. Lead will boil at 1740 degrees, 5500 degrees is the surface of our sun. The surface of Sirius alpha (a very hot star) 32000 degrees. 300.000 degrees is the estimated temperature of the detonation of the atomic bomb on Hiroshima. The sun’s core is around 13.6 million degrees. So 5 trillion degrees is almost 400.000 times hotter than the core of our sun. That would make a nice suntan. “How would you like you flesh? Well done sir.”
A pressure of 1030 is hard to understand. We know that at the surface of the earth the pressure is around 1 kilogram per square centimeter or 1 Bar. When we dive into the water, the column of water above us will add extra pressure due to it’s weight. For every 10 meter we dive deeper 1 Bar of pressure will be added. So when we are at a depth of 20 meter, the pressure will be 3 bar (20 meter water + 1 for the air) The best manned military nuclear submarines can dive to a depth of around 600 meter. This means a pressure of 61 bar. Research submarines, also manned, have been known to dive to depths around 6500m. (The japanese Shinkai 6500). Unmanned submarines can dive to the bottom of some of earth’s deepests oceans (Here the Kaiko holds the record of 10.000m). This means they can withstand a pressure of 1000 (103) Bar. Let’s stick to this analogy and see how deep an ocean we would have to dive to create a pressure of 1030. The ocean has to be 1029 meter or 1026 kilometer deep. This is quite deep as the distance from the Sun to our earth is around 149.6 million kilometer (1 Astronomical Unit). The distance from the Sun to pluto, the farthest planet in our solar system, is 39.5 AU. So we would need an ocean that would reach far past pluto. It would even be billions of times deeper than that. That is dazzling indeed.
The next dazzling number is the distance between the particles that are created, 10-13 centimeter. So what is a very thin object that we can still imagine. The human hair. A human hair in average is 100 µm (one hundredth of a centimeter) wide. If we cut an average human hair in half, it would be 50 µm thick. Would we do this again it would be 25 µm and so on. So how many times would we have to slice the hair to get a thickness of 10-13 cm? If we take the hair and slice it in two exact halves every time, we have to slice the slices 37 times to create a hair of around 10-13 centimeter. Ofcourse at that time we are at subatom sizes which makes slicing a bit difficult.
Hopefully you can better imagine the impact of these numbers by now. Or at least understand that the research on quarks, muons, gluons, bosons and other exotic particles combines extremities of all areas of physics.
Source: Scientific American, issue may 2006, the first few microseconds, Micheal Riordan and William A. Zajc