Every year, just like you, I have a “birth day,” a misnomer as I am not born on that day every year, although I was once. When people ask me why I don’t like to acknowledge my birthday I tell them that time is a continuum. It breezes from one tiny fraction of a second to the next without counting where (when?) it has been or where (when?) it is going. There are no fractions of seconds, of course. We made seconds up and when those were too large, we fractionated them into as many decimal bits as we needed. We made minutes up at some point, perhaps when hours seemed too long or work seemed too slow. We made hours up when the days passed like sap in the wintertime. Days, weeks, months and years were strongly suggested by planetary, lunar and solar phenomena. To our credit, we noticed these patterns and live our lives waiting for them to begin – or end – a hard day, a boring hour-long meeting, a cold winter, a hot-and-muggy summer, the wet season, the dry season, etc. For a nice review, have a look at this.
Typically, though, we don’t think of times much shorter than 0.17 seconds. That is approximately the time it takes to count each of the six beats (or in poetry, “feet”) in “one-Mississippi,” etc. The “one” gets sort of two beats and the “Mississippi” goes in four. If we are keyed into a speed sport, we may split things down to the tenth of a second – I’m not sure I can do this, but I’m relatively certain that people who judge these kinds of events may have a refined sense of one-tenth of a second. Then it’s down to the hundredths of a second and, although all sorts of stopwatches and “photo finish” timers work in that realm, I can’t imagine that the human mind can honestly do much more than watch as the hundredths accumulate into tenths.
There are many time intervals that are extremely difficult for humans to comprehend, though, very short and pretty long. At one end of the range, we have a unit developed in physics called Planck time, named after Max Planck, one of the brilliant theoretical physicists of the 20th Century. This unit is defined as the amount of time that it takes for light to travel one Planck length in a vacuum. A Planck length (not a piratical plank length) is very short indeed: 1.616199×10−35 meters (m), which is about 1×10−20 the diameter of a proton, which is very tiny and comes in somewhere between 0.84×10−15 to 0.87×10−15 m. It is conceived of as the shortest theoretically measurable length within an order of magnitude (or a factor of 10). How much time is a Planck time then? It is a mind-bendingly brief 5.39116×10−44 seconds. Let me show you a comparison between numbers. First, we have 1/10 second:
0.10 or 1/6 second 0.17 (the “Miss” in “Mississippi,” let’s say)
Now, let’s show a Planck time:
To say that differently, but not necessarily more helpfully, there are about 2×10+43 of these Planck times in one second (simply the inverse of 5.39116×10−44 seconds), which is obviously a huge number (2 followed by 43 zeros). The links for Planck time and length will allow you to explore this matter more thoroughly, but both use the speed of light (c=3.00×108 m/s), the gravitational constant (G=6.674×10−11 N⋅m2/kg2) and Planck’s constant (actually, the reduced Planck’s constant, which divides Planck’s constant by 2π), which is 1.054571800(13)×10−34 J⋅s. All this to say something quite simple – Planck time (and length) is derived in a fairly straightforward way using some well-established physical constants, although with some very careful consideration by Dr. Planck. His considerations have held up well; Planck’s constant is part of any useful high school chemistry or physics curriculum.
The real takeaway here is that time and action are inextricably linked. For a Planck time to elapse, a Planck length must be traversed by a photon in a vacuum. A photon must start somewhere and, on its way to somewhere else, it must etch a Planck length in space. This linkage is pretty neat, however resolutely transfixed and “motionless” the avid reader may be in their chair. How can I say that? Are we ever still? No.
Consider the amount of time it takes to absorb one photon of the appropriate energy into the electronic shell of an atom. The photon is either moving at the speed of light (in a vacuum) or somewhere close to this speed if it is traveling through a non-vacuum medium. This modified speed of light is calculated by dividing the speed of light (c) by the index of refraction (n). The higher n is the slower the modified speed of light. Here’s a table of diminishing speeds of light:
|Material||Index of Refraction|
|Ethyl Alcohol||1.36||220,435,631 m/s|
|Crown Glass||1.52||197,231,880 m/s|
|Light Flint Glass||1.58||189,742,062 m/s|
|Dense Flint Glass||1.66||180,597,866 m/s|
|Gallium phosphide||3.50||85,714,285 m/s
If the energy of an atom and the energy of a photon, moving at whatever speed after going through whatever medium, are compatible, the photon is absorbed by the atom with an electron quantum leaping proportionately. This process takes about 1 femtosecond or 1x10−15 seconds (or 0.000000000000001 seconds). There is some infinitesimal distance involved in these transitions, but the distances, if they are meaningful at all, are on the order of Planck lengths and do not add meaningfully to the time it takes a photon to be absorbed.
After that absorption occurs, a new cascade of intra-atomic events occur, each with an associated time, each a tiny bit longer, slower, more human-paced, than the absorption event. I would enumerate them, but instead, I’ll just use a picture, a table and a video for your edification.
|Transition||Time Scale||Radiative Process?|
|Internal Conversion||10-14 – 10-11 s||no|
|Vibrational Relaxation||10-14 – 10-11 s||no|
|Fluorescence||10-9 – 10-7 s||yes|
|Intersystem Crossing||10-8 – 10-3 s||no|
|Phosphorescence||10-4 – 10-1 s||yes|
The other completely nuts thing to keep in mind is that every single molecule and ever single atom in your body is vibrating and rotating – continuously! Every molecule we breathe, eat, digest, incorporate into our teeming collection of collaborative molecules is doing exactly that same thing. Here is a set of nifty .gif images to help you imagine the critical turmoil going on inside (and around) us all:
These represent the different modes of vibration along covalent bonds. In addition to this motion, there are the rotations of each atom at the ends of each bond – and these modes of rotation get complicated really quickly, with spin orientations and precessing (this is what a top does when it spins – the wobble is precession) around axes. It’s all really a maddening, continuous mechanism of complexity. Even if all these molecules inside us were cooled to absolute zero, the motion would continue, although slowed. And all of them are like tiny clocks running at tiny fractions of a second – at an astonishing rate of speed, at roughly 10,000,000,000,000 to 100,000,000,000,000 times per second.
But I am writing about time, not intra-atomic events, and we could all easily be lost inside an atom for the rest of time if caution is abandoned. It is part of the definition of being a chemist – getting lost in the atoms (or at least the molecules). And with phosphorescence events taking a tenth of a second (1×10-1 seconds (or 0.1 s)), we’re at the interval for phosphorescence and can almost comprehend this.
Let’s move on.
Human lives are measured in seconds as well. Nine months of gestation is 23,328,000 seconds (give or take); ask any mother and she will be able to vouch for the satisfaction and endlessness of each second. We go to first grade at 6 years or 189,216,000 seconds and graduate high school after 567,648,000 seconds. Lives get into a murky middle bit after this and people hit benchmarks at various times, but it all comes down to life expectancy in the end. The people in Monaco, one of the richest in the world, have an average life expectancy of 89.52 years, which is 2,823,102,720 seconds – almost 3 billion seconds, people, while the people of Chad, bordered by Nigeria, Niger, Libya, Sudan, the Central African Republic and Cameroon, have a life expectancy of 49.81 years – 1,570,808,160 seconds – very close to being half the average life expectancy of people in the Principality of Monaco, bordered on three sides by France and on the fourth by the Mediterranean, home of casinos, yachts and the Grand Prix. In the United States, average life expectancy is 79.68 years or 2,512,788,480 seconds, 311 million seconds less than the average citizen of Monaco; when stated that way, it seems like a huge difference, doesn’t it?
But we’re not done measuring out human life. In the U.S., we count forward from 0 (zero) B.C. and are currently in the year 2016 as I write this. Two thousand and sixteen years is composed of 63,576,576,000 seconds, only about 22.5 Monaco lifespans ago, but 40.5 Chad lifetimes ago (sort of crazy when you consider it that way). But B.C. (or B.C.E., the term used by anthropologists and anyone studying world history instead of Western European and Middle Eastern history) is just a convenient temporal interrupt in a much longer series of events.
Our species crept into the genome around 200,000 years ago – a time that dwarfs the 2,016 years B.C.E. by two orders of magnitude or roughly 100-fold (100 x). Two hundred thousand years is a whole bunch of seconds – 6,307,200,000,000 seconds, or six trillion three hundred seven billion, two hundred million seconds (the time seems more awesome when typed out as words). But we’re not done yet. Anthropologists have found lots of bones of our ancestors, our nearest relatives to the great apes appearing between 6 and 7 million years ago, 30 to 35-fold more time than for the slow evolution of Homo sapiens, or between 189.2 trillion and 220.8 trillion seconds ago (keep in mind that the 0.2 and 0.8 in those number represent 200 billion and 800 billion seconds).
But let’s keep going. The Cretaceous–Tertiary (K–T) extinction occurred around 65 million years ago; current theories favor a huge meteor striking the earth in the northern Yucatan peninsula; 2,049,840,000,000,000 seconds ago (2 quadrillion seconds). But the earth is believed to have coalesced from hot gases and particles of stardust into something like its current orbit around the sun around 4.5 billion years ago; various models move the digit after the “5” around (is it 4.49 or 4.54?), but there is general scientific consensus around the 4.5 billion figure. 4.5 billion years equals 141,912,000,000,000,000 seconds quadrillion seconds ago, and it was not a livable planet at the time.
The universe, on the other hand, is yet another order of magnitude older. There are at least five models for its age, but the weighted mean of these models puts the age at 12.94 billion years, thus giving the earth about 8 billion years to coalesce into the nasty, raging bit of heat that cooled to what we know and love now. If you do the dimensional analysis here (as I have done so often above), you get a universe that has been in existence creating stars and galaxies and solar systems and planets and moons and asteroids – and that continues to do all of those activities VERY actively right up until today – you get a universe of 408,075,840,000,000,000 seconds (408.1 quadrillion seconds). The universe has been in existence, plus or minus 2.3 billion years or so (see the link above) for 162,399,598.4 average American lifespans (one hundred sixty-two million three hundred ninety-nine thousand five hundred ninety-eight point four lifetimes).
Why have I taken you through a journey from Planck time to the age of the universe? To suggest two thoughts:
- When humans try to imagine events in time, all of us start getting a little foggy about the whole business when it exceeds one of our average lifespans; even then, it is a rare twenty-year-old that can imagine what it means to be forty or sixty or eighty and the eighty-year-old increasingly feels that everything happened “as if it were yesterday.”
- While I have divided up time into fractions of seconds at one end of the scale (the Planck time) and quadrillions of seconds at the other end of time, time is not a series of discrete events; it is continuous and seamless. If one divides a Planck time by another Planck time, the fraction of a second gets shorter – it is about 1×10-89 seconds. One can keep doing this – infinite divisibility – and never reach the continuous nature of time; it will always result in smaller and smaller fractions of time with seamless continuity of the asymptote.
It is entirely possible that we are at the measurement limits regarding the start of our universe. Our current measurements are “birth-of-universe-dependent,” that is, the phenomena that we measure to determine its age are all related to the birth of this universe, the one in which we are a tiny particle orbiting a tiny sun in a tiny solar system in a huge galaxy, which is one of countless huge galaxies (we keep on finding more galaxies) that comprise the universe as we know it SO FAR. Stephen Hawking currently hypothesizes that our universe is one such event in a multiverse. Consider a near-infinitely dense point somewhere in space-time (a “singularity”). From time to time, the density becomes too dense for the singularity to contain it and it “burps” out superfluous matter into space-time, but not in the plane and/or dimension of our universe. Sometimes, these burps are tiny and are reabsorbed by the singularity, but sometimes a new universe of some magnitude buds off and starts expanding. For additional erudition on this idea, please watch the following videos:
This is heady stuff and nearly impossible to understand, except through metaphor and analogy, without the help of advanced mathematics and profound amounts of deep thought (I am a mere chemist and find that I am boggled by these concepts, but I will not deny their allure (p.s. a mere chemist is different from the mythological mer-chemist)).
I will not get into how long this, our, universe is likely to exist. It is an imponderable but is being pondered. Let’s leave the future to those who speculate on those matters (cosmologists and physicists).To conclude, time is a dimension that is infinitely brief (or continuous) and infinitely long (or continuous). Dividing it into human events is convenient, but none of us should pretend that we understand it except by comparing it with events in our own lives. This is not always true; anthropologists, paleontologists, cosmologists, physicists, geologists live on a timeline that, by nature of their study, makes more sense to them and is relatively unlimited by average lifespans and birthdays. We should be humble when we consider the enormity of what has been observed and consider the enormity of what has been observed and consider carefully what is known while allowing that we are not done observing and trying to learn and probably will never finish unless we cease to exist altogether.