The arrow of time

Have you ever wonder what exactly is time? How do we measure time?

The fact that we can measure or even define time at all is that there are changes in our environment. We measure time by oscillations of objects that are repeatable at a constant rate, meaning periodic - for example, the swinging of a pendulum, the 'rise and fall' of the sun, and the vibration of quartz crystals. If nothing changes, how do we measure time? Is there even time in the first place? Hmm ...

Changes can be classified into 2 types: the reversible changes (sort of those which I have described in the previous paragraph) and the irreversible changes. An example of irreversible change is the cracking of an egg, think humpty dumpty (all the kings' horses and all the kings' men, couldn't put humpty dumpty together again).We cannot exactly rearrange the molecules of the cracked egg back to its original form. There are tonnes of irreversible changes : flowers wither, we grow old. It is these sort of irreversible changes that points the arrow of time.

A more rigourous way to describe these processes is by using entropy, $$S=k_b\text{ln}\Omega$$ , the measure of disorderness. The second law of thermodynamics says that the entropy of the a close system tends to increase or remains the same. $$\Delta S=Q\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\geq 0$$ . To put it simply, a system will tend to become more disorderly; a nicely stacked paper will tend to get untidy. But why?

Because the number of possible ways for being untidy, the papers scattered in many different ways, is more than the number of ways of being orderly - stacked up nicely, one on top of another. Let me illustrate using another example. There are so many different connecting cables that joins up my computer, keyboard, mouse, modem, CPU ... that makes them function properly. There are very many possible ways of connecting them in the wrong way, but the number of ways to connect them so that the computer works properly is very limited by contrast!

Therefore work needs to be done to 'restore' the state to a lower entropy. That is why sweeping the floor of scattered papers and arranging them in order is hard work!

...... ok, this is hard work ...... I shall rest and let the expert do the talking ...

So I have embedded the 2 videos by a cosmologist Sean Carroll who can provide some possible enlightening answers to the questions on time.

Part 1 of the video is on the basics of entropy. A really good introduction!

Part 2 of the video discusses how entropy is applied to our universe and daily life. Really really cool stuff!!!

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