# Give an arrow to time

I'd like to ask about the meaning of the following sentence from "The Science Delusion" by Rupert Sheldrake

"This increase of entropy gives an arrow to time, and means that spontaneous processes are always running 'downhill' from a thermodynamic point of view".

The first part of the sentence is unclear to me. So far I have been unable to find no idioms with "give an arrow" so I presume I should consider only literal meaning which is rather vague for me. I hope it is not necessary to be a PhD in physics to understand it. The only one reasonable guess I can think of is that it's another way to say that the time is limited thought I'm discontent with how it coincides fully with the 'arrow' metaphor.

• The "arrow of time" is a metaphor for direction. Basic physical laws work the same forward and backward, so it's a problem to explain why real-life processes are obviously not symmetrical with respect to time. Apr 16, 2017 at 9:42
• In that respect I'd say the time is always irreversible or asymmetrical disregarding whether we have entropy or don't. Or is the sentence telling me that entropy makes the time asymmetrical? Apr 16, 2017 at 9:57
• Or is the author saying that the time is asymmetrical because of entropy ? Apr 16, 2017 at 10:05
– NVZ
Apr 16, 2017 at 10:47
• How can entropy, "a lack of availability of thermal energy for conversion into mechanical work" provide an arrow to anything?? Isn't an arrow pointy?? Apr 16, 2017 at 11:59

The expression refers to a problem in physics. If you were to watch a movie of a small number of particles interacting (e.g. molecules of gas bouncing off each other) then you could not tell whether the movie was running forwards or backwards: the equations that govern the particles work equally well in both directions. In this sense the equations do not have an "arrow of time" telling you which way time goes; you can switch the direction of time and everything still works exactly the same.

However if you were to watch a movie of thousands of molecules of two gasses, starting with all of gas A on the left and all of gas B on the right, you would immediately see that the film was running forwards as the molecules mixed. If it was run backwards you would see the two gasses "magically" separating.

So there is a paradox: somehow the "arrow of time" emerges from the collective behavior of the gas molecules rather than their individual behavior. "Entropy" is the technical term given to the degree of randomness in the situation. Roughly speaking, the start state with the gasses partitioned has less entropy than the end state with them all mixed. The mathematical definition is about the possible number of places all the molecules could be: obviously if the gasses are separated then the molecules of gas A are constrained to be on the left. But once the gasses are mixed then any molecule of A could be anywhere. Likewise for gas B starting on the right. So the end state has more possibilities than the start state.

• Thank you Paul Johnson for the elaborate answer. I would have never guessed that depth in seemingly plain phrase! To me it looks more like philosophy than physics and I like such pearls of meaning in the languages. Apr 16, 2017 at 18:31