Scales of time
To put our remarks on persistence into perspective, let us now review the temporal scales associated with various physical processes.
The Planck time
As physicists probed elementary particles with greater and greater energies, they realized that as energies increased, the timescales for the processes that they were investigating decreased.
There are several ways of understanding this reciprocity. For instance, de Broglie’s relation E = hv shows this explicitly. Here E is the energy of a particle, h is Planck’s constant, and v is the frequency (a reciprocal time) of the associated de Broglie wave. We shall explore this reciprocity in more detail later on in this book. Suffice it for now to say that most physicists would agree that there is a limit to shortness of duration, to how quickly we can perform any action. Below a certain scale, there seems to be no physical or theoretical meaning to intervals of time. This limit is generally called the Planck time, denoted TP. It is a heuristic concept used extensively to motivate research in speculative areas such as string theory and quantum gravity.
The Planck time is assigned a value from dimensional analysis via the following heuristic argument. Modern physics is based on several fundamental constants, three of which are c, the speed of light, ft, Planck’s (reduced) constant, and G, the Newtonian constant of gravitation. From dimensional analysis, it is easy to work out that ftG/c5 has the physical dimensions of a time squared. Dimensional analysis does not give us any numerical factors, so taking the overall numerical factor to be unity, we define the Planck time as
Such a timescale is far, far smaller than any timescale encountered in the laboratory (these are discussed next). It is commonly believed that the Big Bang, the origin of the universe, took place over such a timescale.
The concept of Planck time and the related Planck scales of length and mass have been criticized by Meschini [Meschini, 2006].