Letter: How much is time?

From Alan Fowler

In Vlatko Vedral’s excellent essay suggesting that an ultimate theory might emerge from thermodynamics (13 October, p 32), he recalls Max Planck describing his idea that energy comes in discrete chunks as an “act of desperation”. Planck also anticipated Vedral’s argument.

In a 1909 lecture entitled “The Atomic Theory of Matter”, Planck discussed reconciling the observation that “the micro-changes of state are reversible” with the observation that “the macro-changes of states are irreversible”. He posed the question: “How many atoms are at least necessary in order that a process may be considered irreversible?” He answered it: “So many atoms that one may form from them definite mean values which define the state in a macroscopic sense.”

So the arrow of time applies to ensembles containing enough atoms that an average state is meaningful: which is to say when thermodynamic calculations can be done. That makes it easier to understand the paradoxical consequences of energy that comes in discrete chunks, such as the difference between the future, with its particles in multiple possible states, and the past, with its ensembles in singular states.

At last, a rational approach to physics. No multidimensional flights of fancy for Vlatko Vedral. No mathematically beautiful symmetry. Things are as they are because energy only flows from hot to cold, not from cold to hot.

• Oops. We misspelled the last name of Vlatko Vedral when we were reporting David Deutsch’s theory of everything last week (10 November, p 5).

Edinburgh, UK