Cosmic Energy-Time Diagram

The Duration and Total Energy of Sub-Atomic, Human and Cosmic Events

Most events have an associated duration and energy, and can therefore be located on a diagram of this kind. As usual, we use exponential axes, with 45 x 85 factors of ten range in time and energy. Units of time are seconds (with smaller & larger units on the top axis), while units of energy are Joules (a kg bag of sugar dropped 4 inches; with corresponding units eV for the quantum world, and tons of TNT explosive equivalent for the cultural world).

Starting with the humanly intuitable world (pink): a kg of chemical fuel can release ~1 MJ energy slowly (lunch digested over a few hours) or rapidly (a kg of TNT can destroy a car -- much like a car crash). Of course, the rate of energy release is "power" -- measured in Watts = Joules/sec. Lunch is 100 Watts for a few hours, a car crash is a mega-watt for a second. At the upper limit of intuitability is the rapid release of a billion Joules (lightening strike, or 100 kg TNT), or the sustained power of a 1 km sized region of a storm. At the low end, one barely notices the workings of a wristwatch (µW) or a single spoken word.

Beyond the human realm are single nuclear weapons which individually detonate within a microsecond -- although a global exchange might take an hour or two to unfold. As a nuclear weapon is to a lightening strike, so a 10km asteroid impact is to a nuclear weapon (the kind which causes major extinctions). Slowing the Earth's orbital motion over a year would release about 1/100 solar luminosity for that year. The Earth's rotational energy is much less, and is being transferred to heat and the moon's orbital energy on a cosmic timescale.

Further up the scale is the realm of stars -- with total energy reserves of 1/10 to 100 M of hydrogen buring at 0.7% total efficiency (ie Efuel = 0.007 x mfuel x c2). This yields 1042 - 1045 Joules, released over 1011 - 106 years at powers of 10-4 - 106 L. The straight line linking stars of different mas is derived from the mass-luminosity relation for main sequence stars.

For the largest energies, one turns to gravity. A stellar core collapse releases about as much energy as all prior nuclear burning, but on a 10 ms timescale -- giving it a luminosity greater than all stars in the visible universe, for those 10 ms (similar reasoning places GRB's in the same region). Accretion onto black holes can yield 1012 L for 10-100 Myr, while the energy of cluster formation, and subsequent cluster mergers release even more energy on Gyr timescales (some of which is later radiated as X-rays by the hot gas).

Down in the quantum world, the Planck relation E t ~ h defines the photon line (ie E = h ). At corresponding energies and timescales are atomic nuclei; atoms; and molecules. Chemistry, for example, functions at fractions of an eV on timescales of nanoseconds. Nuclei undergo changes of MeV energy on timescales of 10-20 sec.

Intuitively linking these three basic worlds -- atomic/human/cosmic -- is quite a challenge. Let's try. There is as much exponential gap between an atomic orbital time and us saying "hello", as there is between us saying "hello" and geological (mountain building/eroding) timescales. Imagine you are an electron in orbit, watching yours colleagues in their own orbits. Looking out into the external world with your telescopes, you see a gigantic person's mouth -- apparently frozen in "mid-word". Studying it, you estimate it takes 100 million of your years to say the word "hello" -- what a slow conversation -- mountains grow and erode before the sentence is finished. Of course, we "feel" those words to pass quite quickly -- but as we hear those words, as much has happened in the atomic world as we might feel to have happened since pangea split and the atlantic was formed.

Conversely, imagine you are a solar type star, chatting with your stellar colleagues. Using a powerful microscope, you study the "microbes" residing on a small "rock" in your vicinity. They grow and die every 30 seconds, generation after generation. Throughout their lives, their mouths constantly form words, each word lasts 10 nanoseconds. To the stellar you, the human world functions on the atomic timescale; while to the atomic you, the human world functions on the stellar timescale. While our brains can barely cope with half the jump between atomic and cosmic, don't forget that these cosmic structures function via atomic processes -- the nuclear burning in stars; the bremmstrahlung radiation from galaxy clusters -- all occur at the atomic level.

Finally, this unimaginable gulf between micro and cosmic timescales can give us a glimpse of why living things can be so stunningly complex. The Earth provides an environment which is stable over enormously long cosmic timescales, and within that environment chemical reactions continuously occur at the dizzying speed of the microworld. It is perhaps just possible to grasp how evolution has bridged the inanimate and animate worlds -- she works unimaginably fast for an unimaginably long time.


An animated power point slide of this diagram can be found [here]. With successive clicks, the diagram is built up roughly following the descriptions given above.

Figures made for "Designing Matter" Lectures, (by me).