CHAPTER 3: TIME
“Time” is actually difficult to define, but can be understood to be that which can be measured with a “clock”.
In turn, a clock is any device based on regular recurring motion (e.g. a spinning body, a swinging pendulum) or easily repeatable motion (e.g. “hourglass”).
Recall that our “second” was originally defined as 1/86,400th of the time it takes the Earth to rotate on its axis. Since we have adopted the second as our “time standard”, we express all other amounts of time in terms of seconds or accepted multiples of seconds (days, years, etc)
It’s also important to realize that we use the word “time” in two different ways: (i) “instantaneous time” is attached to any particular moment in time (e.g. 12:00:00 midnight on 01/01/2000); and (ii) “elapsed time” is used to record an interval of time between two instantaneous times. (We can almost always tell the difference by the context, so this is usually not a problem.)
In physical science, elapsed times (i.e. time intervals) are probably referred to a lot more often than instantaneous times.
Time is often referred to as “the 4th dimension”, e.g. in the context of relativity theory. But time isn’t like a spatial dimension in that time has an “arrow”. That is, time only flows one way. One can travel forward or backward through space, but time only increases. The concept of “time travel” (travelling backward in time) is a popular theme in science fiction, but there are both physical reasons and philosophical reasons why this is unlikely to be possible.
THE SPACE-TIME CONNECTION
We tend to see our world in instantaneous “snapshots”. Literally, we “see” because our eyes take in light. But light travels incredibly fast (about 3.00 ´ 108 m/s). Because the light reaching our eyes from everything within our normal visual range arrives simultaneously, we tend to imagine that the events we are witnessing are also simultaneous, i.e. that the light has travelled instantaneously. For most everyday observations, this “error in perception” causes no real problems, but we must not think this way when we are considering the universe on an astronomical scale.
When viewing distant stars and/or galaxies, the distinctions between space and time become seriously blurred. Light reaching us from very a distant source is also light which left that source in the very distant past.
This is one reason why the “light year” is a useful unit of distance. The light from a star 1 million LY from Earth has taken 1 million years to reach us and is therefore “a million years old” when we see it.
As a result, we can never see the universe as it is at this moment! Rather, the light entering our eyes at any one instant comes from many different sources. So, it has traveled many different distances and left these sources at many, very different times. So, what we see as “simultaneous events” are really “superimposed images” of events which actually occurred at completely different times.
In astronomy, it must be remembered that, literally, “far away equals long ago”!
DISTANCE AND TIME
Since light (as well as other electromagnetic waves discussed later) all travel at a constant speed (c = 3.00 ´ 108 m/s), a very simple and useful relationship to remember is
Distance = Speed ´ Time or Time = Distance / Speed
i.e. d = c t or t = d / c .
e.g. If our sun suddenly burned out, how long would it be before we realized it?
e.g. When Venus is at its closest point to Earth, a radio beam sent from Earth and reflected from Venus returns to Earth in about 300 s. How far away is Venus at its nearest point?
THE EXPONENTIAL SCALE OF TIME (INTERVALS)
10-16 s time for one orbit of an electron around
a hydrogen nucleus (called an “atomic year”!)
10-15 s current shortest time interval of a laser pulse
(10-15 s is called a “femtosecond” or fs)
10-13 s typical vibrational period of an atom within a
solid
10-5 s high speed electronic strobe, flash or frame
speed (e.g. used to “stop” the motion of a bullet)
10-3 s digital camera flash
10-2 s frame speed of movie or video camera; AC
period
101 s 100 m sprint standard; the Earth minute
103 s Earth hour
104 s Earth day
107 s Earth year
1015 s time for rotation of Milky Way galaxy (called a
“galactic year”)
1017 s current estimate of age of the universe
THE SPACE-TIME CONTINUUM
In most everyday life situations, we can think of space and time as distinct, but in more extreme conditions (high speeds, large masses, strong gravitational pulls) these distinctions can break down. According to Einstein’s special relativity theory (1905) and general relativity theory (1916)
1. Events seen by one observer as “simultaneous” may not seem so to another.
2. Different observers moving relative to one another will measure different time intervals between the same events and different lengths for the same object.
3. A body’s mass will increase as its speed increases dramatically.
4. Large masses (like stars and planets) actually “distort” the space and time around them, causing changes to the paths of moving bodies and to measurements of time by different observers.
It can therefore sometimes be useful to think of space and time together as forming a 4-dimensional continuum (3 spatial dimensions and 1 time dimension).
There’s a problem, though! We can’t visualize or represent something which is 4-dimensional within our 3-dimensional spatial world. So, to make things simpler, we sometimes “suppress” one or two of the spatial dimensions.
On the graph on p. 85 of the text, we imagine the space-time continuum associated with a world that has only one spatial dimension (e.g. a north-south line).
Each point on the resulting graph consists of a time coordinate (horizontal axis) and a space coordinate (vertical axis), and the graph therefore displays changes in both location (up or down) and time (to the right only). Note that even if you don’t move in space, the graph continually shifts to the right in time. Such a graph can show an object’s “trajectory” in space-time, and is sometimes referred to as its “world-line”.
We may well have occasion to return to “space-time” or to “special or general relativity” theory in some of our future discussions related to astronomy or gravity.
NOTES ON THE “DAY” AND “YEAR”
1. The “day” we have been referring to is actually a “solar day” (the time between, say, the Sun’s zenith on successive rotations of the Earth). In fact, the Earth must rotate about 361° during each “solar day”: 360° for one complete rotation on its axis, plus an additional 1° to account for the Earth’s movement around the Sun (which covers 360° every 365 days, or nearly 1° per day). Refer to the diagram on p. 87.
The time for a simple 360° rotation of the Earth on its axis is actually called a “sidereal day”, and is about 23 hr, 56 min (since the extra 1° rotation in a “solar day” takes about 4 min. You are not responsible for the sidereal day, though this is an important unit of time for astronomers.
2. Our currently accepted 365-day year is slightly out of sync with the Earth’s actual orbit of the sun. In fact, it takes just under 365.25 days to complete one orbit. Over a number of decades, this would begin to cause problems with the timing of our “seasons”. For this reason, we add an extra day every four years (called “leap years”).
Even this adjustment slowly drifts out of sync, since the actual orbital period is 365.2422 days. Consequently, the globally-adopted “Gregorian calendar” specifies that occasional leap-years are to be skipped—to be exact, those “century leap years” that are not divisible by 400 are omitted. Thus 2000 and 2400 (being divisible by 400) was and will be leap years, while 2100, 2200 and 2300 will not be leap years.
SOME FINAL REMARKS REGARDING THE DISCUSSION OF TIME IN THE REMAINDER OF CHAPTER 3
1. You aren’t responsible now for the material in the text on seasons, the zodiac, the moon’s phases and eclipses (p. 90 – 101), though a little of this material may be accessed in answering class questions later.
2. You are strongly encouraged to skim through the entire section entitled “History of the Universe” (p. 102 -151). We will refer to some of the earlier history (p. 103 – 120) a little later in our discussion of matter (Chapter 4) and also in answering some class questions related to astronomy. While certainly interesting, much of the material from p. 123 – 140 relates to biological science (living things, which aren’t directly part of this course), though we will touch on some geological aspects of this period (e.g. “plate tectonics”) a bit later. Most of the last section (p. 141 – 151) has essentially been covered already in our earlier discussion of historical milestones.