Powers of Time: Time Scales of Life, the Universe, and Everything in It.

Scales of time can range from about 10E-44 of a second which is 'Planck Time', and up to several billions years which is the age of the universe. How do we relate time scales to physical processes? This lecture was introduced at 'Time: Between Science and the Arts', a conference held at the Bloomfield's science museum in Jerusalem, June 2008.

Charles and Ray Eames in 1977 created a short documentary film (based on a 1957 essay by Kees Boeke) that showed us the beauty of the Universe at all its space scales.  The film, later produced as a book, ‘zoomed’ through 42 orders of magnitude of size, from sub-elementary particles up to the whole Universe. 

The rates of measured, calculated, or imagined processes cover more than sixty orders of magnitude – less easily illustrated but no less fascinating and ‘beautiful’. (Actually, an infinite number of orders of magnitude, since I consider that “imaginable”.)  For much of the range, every third order of magnitude (power of ten) has been given a (sometimes picturesque) name, ranging from a ‘zeptosecond’ to ‘googol years’.

I survey these rates, or durations, zooming from the shortest physically meaningful time – a concept I discuss briefly - out to the longest useful time, the projected (though disputed) lifetime of our Universe.

 Cyclic and Non-cyclic processes

Processes may be described as:

cyclical, in which the system returns periodically to exactly the same state, or very nearly so, as for instance electrons circling a nucleus, or menstruation: characterised by cycle time;

non-cyclical, microscopic processes of radioactive decay or decay of elementary particles; macroscopic processes driven by the Second Law of Thermodynamics, such as the melting of an ice cube; and cosmological processes that start with the Big Bang (though see below): characterised by half-life or total duration;

 and quasi-cyclical, as in a spiral, with the system returning periodically to nearly but not exactly the same state.  In a sense, life itself falls into this category: Individual lives end, but the species continues.  Such processes are characterised by cycle, or generation, time, but with a slowly changing character and perhaps an overall ‘half life’ or total duration. In my sketch, for simplicity, I include these in the “non-cyclical / non-cosmological” category.

My survey is of course not systematic; I try to give a feeling of where we are in the temporal universe by touching only on highlights, especially those relevant to life.

The figure shows where some of the highlights of our Universe and its contents fall into the big picture of rates and durations.  The picture depicts time running logarithmically upwards.  It has columns for the time in powers of seconds accompanied by their names, and by a years scale where appropriate.  The processes are divided into those that are cyclical, where the time is that of a single cycle, and non-cyclical, where the time is either the total life or, if the process or element dies exponentially, its half-life.  The non-cyclical processes are further divided into cosmological, where the time is that from the Big Bang (assuming that model of the Universe); and non-cosmological.

Shortest time

Surprisingly, there is a “shortest time”, and this is the starting-point of the figure. This time is the “Planck Time”.  It is, in principle, the minimum measurable time, for reasons related to the Heisenberg Uncertainty Principle.  That is, specifying times shorter than this has no physical meaning.  Its value is 5x10E-44 sec.  In practice, of course, we are very far (some 28 orders of magnitude!) from measuring times this short, but this does not stop the cosmologists from specifying times close to this limit in Big Bang models.

Processes relevant to life fall in a narrow range well above centre on the logarithmic scale from fast to slow, or brief to long.  [In the space dimension life-relevant sizes fall into a narrow range two-thirds of the way up – on a logarithmic scale – from the smallest meaningful length, the Planck Length, to the radius of the Universe.]

Infinite love

I end the figure (at the top) with infinity, essentially because I am in love with the concept of infinity. (So are many mathematicians.) It appeals to me philosophically, emotionally (perhaps because of my wish for immortality), and in the cosmological context:  I am much more comfortable with a universe that always has been and always will be, than with one that started with a “big bang”, before which there was neither space nor time.  I prefer the concept of a universe that is cyclic – if there is a big bang, that it be followed by a “big crunch” and a new big bang.  Unfortunately for me, recent observations suggest that there will be no big crunch, that our Universe will expand indefinitely – meaning that we face an infinite, and finally cold and lifeless, future – but a finite past.  (I note that many people cannot bear the concept of infinity in any context!)

June 2008