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I recently read two books by Carlo Rovelli: The Order of Time, and Reality is Not What it Seems. This is some of what I learned.
Physics says Time has an Arrow, which is in fact, the most distinctive feature of Time. The Arrow means Time always runs forward, never backward — the hands of an analog watch (remember those) relentlessly turn clockwise, never counterclockwise.
But is all that really a fundamental truth of nature? Carlo says No.
Time’s Arrow points in the direction of increasing disorder, what we call entropy. The infamous second law of thermodynamics allows only those reactions that increase disorder (entropy) as Time increases.
Entropy is what physicists call an emergent property — it does not exist at the atomic scale, but becomes apparent at our scale, in the macro-world where everything we see is comprised of billions of billions of atoms.
A prime example of an emergent property is temperature, which is a measure of the average kinetic energy of atoms due to their chaotic, thermal motion. A single atom has no meaningful temperature; its kinetic energy can change radically a billion times each second. But when averaged over trillions of atoms, temperature, and entropy, emerge as concepts humans find useful.
Let’s consider an example. Imagine a glass of wine falling off a table onto the floor, shattering into myriad glass shards and splattering wine everywhere — unfortunate, but entirely plausible.
Now imagine a video of this unfortunate occurrence played backwards: shards of glass and drops of wine spontaneously fly together, forming an intact glass filled with wine that flies upward and lands gently on the table. The time-reversed action is hysterically ridiculous, but why?
Newton’s laws of motion (F=ma and all that) are perfectly symmetric in Time, as are all other laws of physics, but one. All physical laws, but one, allow any physical process that proceeds from A to B, to proceed just as well from B to A.
At the atomic scale, Time running forward is indistinguishable from Time running backward. If the video of a falling wine glass is magnified sufficiently to reveal individual atoms, no one could determine whether the video is playing forwards or backwards — every atom’s motion is entirely realistic either way. Only when we observe the actions of billions of atoms, can we confirm that entropy (disorder) increases as Time runs forward and decreases as Time runs backward. Entropy is an emergent property, and it alone defines the Arrow of Time.
Here’s another example. The integers 1, 2, 3, 4, 5 are in a special sequence, as most of us would agree. A person who launches rockets might think 5, 4, 3, 2, 1 is also a special sequence. So, let’s say, of the 120 possible permutations of those five integers, two are special (well-ordered and low entropy).
Now imagine we number five index cards 1 through 5, and arrange them in that order. Let’s then repeatedly shuffle the cards until they are in a random sequence in which every permutation should be equally probable. The probability that shuffling makes the sequence less special is 118/120 = 98.3%. The cards begin in an well-ordered (low entropy) state, and most probably end in a less ordered (higher entropy) state.
If we expand the deck from 5 cards to 13 cards, the number of permutations exceeds 6 billion. The probability that shuffling an ordered 13-card deck makes the sequence less special becomes, for all practical purposes, 100%. This is the basis of the second law — special states are by definition rare; any process that randomly changes a system’s state is immensely more likely to produce a less special state than a more special state.
The second law does not say entropy can never decrease; it says any physical process is immensely more likely to increase entropy than to decrease it. The second law is a statement of probability, which is quite different from the law of conservation of electric charge — we believe charge is absolutely conserved everywhere and always, without exception.
Rovelli says special states — well-ordered, low entropy states — are special only because we say so. Nature doesn’t care whether a wine glass is on the table or splattered across the floor. Neither does nature care about the order of a deck of cards.
Rovelli says entropy, order, and disorder are merely human concepts, like beauty and justice. Such concepts help us organize our thoughts, but none of these concepts has a fundamental natural basis.
Then what about Time?
Whether the Arrow of Time is or isn’t fundamental, I am quite sure I’m not getting any younger — it’s Time for my nap.
More on Rovelli another Time.
Best Regards,
Robert
April 23, 2019
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