Beyond the God Particle (17 page)

Figure 5.6, Space-Time.
The horizontal axis represents all three directions in space, while the vertical axis represents the flow of time.

Alas, space is three-dimensional, and we always have a problem in rendering space—it's impossible to exactly draw three dimensions of space on a two-dimensional piece of paper. Furthermore, we will also have to use one of our two dimensions on the piece of paper to draw the fourth dimension—that of time. So, to depict space and time, we can only draw one horizontal axis to represent all of space, and let's say that this represents the east-west direction—like any map, east goes to the right and west to the left. You have to use your imagination to see the two other axes of space, one representing north-south, and the other up-down, coming out of the page and into your living room. The vertical axis in our picture represents time. In
figure 5.6
we have drawn the basic map. This is a picture of a new world that we call “space-time.”

Now, in nature there's something weird about time that distinguishes it from space. In space, we can always decide where we want to be. If we want to be in Antigua, Guatemala, we can hop a plane and enjoy beautiful coastlines and wonderful coffee, the colorful dress and the kite flying of the local Mayan descendants’ culture. But we have no control over where we are in time. We just “are” someplace in time. Of course, when we “are” at some time, we also “are” someplace in space. In our plot, a definite time and a definite location in space is a geometrical point, a “space-time” point. A point in space-time is called
an event
.

For example, on the afternoon of July 4, 1927, there was an event at which little Billy Johnson lit off a firecracker in front of his father's hardware store on Main Street in Bedford Falls. The firecracker exploded with a loud bang. That particular instant in time at that particular point in space defined an event in space-time: the “firecracker event.”

Our world is a fabric of a countless infinity of events. A mosquito stings Mrs. Fenster on her leg at her niece's ballet recital in the gymnasium of her local high school on September 20, 2003, at 2:31 p.m.; an atomic nucleus of Uranium spontaneously decays at exactly 5:23 a.m., GMT, deep in the exact center of the earth; a supernova explodes eight billion years ago in the constellation Taurus, at a distance of eight billion light-years from the earth; the light from said supernova will be detected by telescope in Chile at exactly 12:09 a.m. local time on January 12, 2015. These are just a few of the countless infinity of events that define our world. Some are in the deep past, others in the distant future. And some are related to one another, like the observation by very smart aliens many light-years away
of the light emitted from the firecracker explosion by Billy Johnson. We might say that physics is the collection of events in space-time and the rules by which they relate to one another.

Figure 5.7. An Event in Space-Time.
This event, consisting of the explosion of a firecracker, is located at some particular value of time (which we have labeled as 1:31 PM, July 4th, 1927) and at some particular location in space (which is directly in front of Mr. Johnson's Hardware store on Main Street in Bedford Falls).

Let's return to Billy Johnson's firecracker experiment. It's convenient to reset our clocks and call the time of the fire- cracker event “zero,” so our “time coordinate” for the firecracker explosion is defined to be t = 0. And, likewise, we reset our space coordinates so that the location of the exact spot at which the firecracker explodes is also “zero,” or, for our plot x = 0. Our space-time plot for the world then looks like
figure 5.8
:

Figure 5.8. Firecracker at Origin.
For convenience, we relocate the orign of time and space to coincide with the event of interest. The event, consisting of the explosion of a firecracker, is relocated to a value of time t = 0 by simply resetting our clocks, and a location in space, now denoted x = 0, by resetting our map coordinates.

Now, when a firecracker explodes, there are physical consequences. If we plot the sequence of events, they look like
figure 5.9
. Of course, there is an instantaneous heating and compression of the atmosphere at the event of the explosion, and this produces sound waves, actually more of a shock wave in the air, the “bang” that emanates outward triggering an infinity of other events. For example, a brief instant later the shock wave reaches Billy's brother Tommy's ears. Tommy Johnson happened to be standing a mere ten feet from where the firecracker exploded out in the street in front
of the hardware store. We label this on our
figure 5.9
as event (A). A brief instant later the “bang” shock wave has spread farther and reaches the ears of Mr. Johnson, who is in the backyard of the hardware store unloading boxes, an event we label (B).

Figure 5.9. Firecracker Sequence of Events.
The shock wave of sound emanates outward in space-time from the firecracker event. We see a shock wave that grows larger in radius at later times. This traces out a cone-shaped surface in space-time. Subsequent events (A), (B), and (C) lie on the cone of the shock wave.

And still another instant later, the shock wave has spread farther and reaches the ears of Ms. McMurrough's two dachshunds that are sleeping in her house down the side street behind the hardware store, at event (C). The sound wave continues outward, fading in strength as the compression
wave of air expands out into the atmosphere. It leaves behind a startled Tommy Johnson; a concerned Mr. Johnson, who hurries toward the front of the store; and two frantically barking and jumping dachshunds that start climbing up the drapes of Ms. McMurrough's house.

Each subsequent event is defined by the time it takes for the the shock wave from the explosion of the firecracker to reach that particular location in space. The firecracker shock wave is expanding spherically out into the atmosphere, growing larger in diameter but weaker in strength as time progresses. On our plot this shows up as a “cone” in space and time. You need to use a little imagination here, since as we've said, we cannot draw all three dimensions of space (we've depicted the top of the cone by a tilted circle to give the impression of more dimensions of space). At any instant in time after the explosion there is a spherical “wave front” of air compression, the shock wave, i.e., the audible “bang,” which we depict by this circle. The distance of the shock-wave-front from the original explosion, x, is just the time from the explosion, t, multiplied by the speed of sound, v
_sound
(that is, distance of “bang” x = v
_sound
times t).

Of course, there's also a flash of light that is emitted by the firecracker explosion. The light travels at c, the speed of light, which is much, much faster than sound, so we can only draw this in a very exaggerated way on our plot. If we also include the light wave in the same plot as the sound wave, it looks like
figure 5.10
.

Note that the light always reaches the distant observers much sooner than the sound wave. That's why these events are so crowded together near the origin, because the light arrives in such a small time interval, but if you look carefully at
figure 5.10
you'll see that these events all happen at the same location in space as the sound events. At event An the light flash reaches Tommy Johnson's eyes. The time interval between event (A) and event (A´) is so short that Tommy hardly notices any time difference between hearing the explosion and seeing it. Mr. Johnson is farther away in the backyard of the hardware store when the direct photons from the firecracker reach him at event (B´), with the sound arriving a tiny instant later at (B). Finally, down the street the dachshunds, though sleeping (well, er, um, dachshunds are never 100 percent asleep), see the flash of light at event (C´) and are alerted, and then a noticeable instant later they hear the boom at event (C), which drives them into dachshund high gear whence they go tearing around Ms. McMurrough's house.

Figure 5.10. Light Sequence of Events.
Light also emanates outward in space-time from the firecracker event. This also traces out a cone-shaped surface in space-time. Subsequent events (A´), (B´), and (C´) lie on the light-cone. Note that each of these events occurs at the same space-location, but at much earlier times, than the corresponding events (A), (B), and (C), due to the fact that the speed of light is much greater than the speed of sound.

The very fast light wave continues to propagate outward through space at 186,000 miles per second. Unlike sound, which can only propagate relatively slowly in the air (about 1,000 feet per second) and cannot go into outer space, the light waves from the firecracker explosion continue far, far
out and away from the arth. Within a second and a half the light reaches the moon, and could, in principle, be detected with an extremely powerful telescope there. About 38 hours later the light reaches the orbit of Planet Pluto; about 3.8 years later the light reaches the nearest star,
ε
-Proxima; about 30,000 years later it has transited the diameter of our Milky Way galaxy; in about 13 billion years it reaches the most distant objects we have ever seen in a telescope, the galaxies whose light is now reaching us as they appeared in their embryonic form, just forming after the big bang.