It's a pop sci analogy, not a rigorous scientific statement. Of course real objects deform, get hot, and lose energy to sound.

But that's the point. Entropy changes. If entropy changes, events are irreversible.

As a crude simplification the less an event leaks entropy, the closer it is to being reversible.

Microscopic events - low-energy atomic collisions and particle collisions - can appear perfectly symmetric in time. So much so that microscopic reversibility is considered a thing in physics and chemistry.

What actually happens is more subtle than that, because quantum indeterminacy makes it impossible to exactly reverse a quantum event. Instead of Newtonian precision you have to settle for a probability density of possible outcomes.

But even so, you can't tell which direction time is running in many particle interactions. The particles aren't altered in any appreciable way, and no information/energy leaks to the surroundings.

So even though the difference between before and after isn't precisely deterministic, you still can't tell whether time is running forwards or backwards, because there's no entropic delta to give you a clue.

One one hand, the analogy is imperfect with billiard balls precisely because they are big collections of particles, not actual particles. It might help to imagine instead a collision of, say helium atoms.

On the other hand, if you see a "video" of two warm, vibrating billiard balls colliding, which then cool off and stop vibrating, it's still only a good guess that the video is in reverse. It's only highly improbable that the motion of the atoms in the billiard ball, air, table, etc cancel out to produce more order, not impossible. That improbability, AFAICT, is the linchpin of the Second Law of Thermodynamics.

It's the old,"A farmer has three chickens that won't lay eggs. So he calls a vetrinarian, and he can't help. So he calls a biologist, and she can't help. So finally he calls a physicist.

The physicist takes copious notes, precise measurements, and spends the rest of the day furiously scribbling in his notebook. Finally the physicist shouts excitedly, and rushes into the farmhouse.

The farmer says, "Did you figure it out?" And the physicist says, "I did! But it only works for spherical chickens in a vacuum."

I thought the canonical version of the joke was about a spherical cow[0].

0: https://en.wikipedia.org/wiki/Spherical_cow

Idealized spherical cows in a vacuum reduce to idealized spherical chickens in a vacuum if you work out the math ;)

I never understood the argument either, but I am no physicist. Start with the table racked (e.g. order) and break. One can easily discern the direction of time as the table goes from order to disorder.

I think that's more because you are familiar with the original ordered state of the racked balls. If you take out energy lost to friction and heat and allow infinite time, after breaking the balls would bounce around ricocheting ad infinitum, eventually forming the racked state momentarily before continuing into chaos. Just like the monkeys on typewriters, and more frequently broken clocks.

By chance yes. But the frequency of events of order to disorder is less than order to disorder, because ultimately, the universe tends towards entropy.

Yes, billiard ball collisions are not actually perfectly elastic, but they are about as close as you are likely to encounter in everyday life.

Usually one would mention that you need to consider the billiard balls as point particles. At least that's how the analogy was given to me.

The point you're missing though, is that even in your example, the backwards case is still physically valid. It is true that no macroscopic interaction is reversible in practice, but this ceases to be the case for a fully defined system where there is no increase in the entropy, and you could argue it is because these do not exist, but there is no physical reason that they CANNOT exist. For one, if you could model all of the energy losses due to vibrations effectively, there's no reason to think that physically one could not use a very precise arrangement of speakers to cause compression waves to converge to the point of contact at the exact instant of the collision and revert the system to the initial conditions. Just because it's backwards doesn't make it physically invalid, except for the friction (and thus heat/entropy thermodynamic part). The backwards scenario still fully obeys the laws of physics. What you're doing here is essentially begging the question by saying that thermodynamics (and thus experience) tells us that these things (elastic collisions) don't happen because they don't happen. What you haven't established, however, is why. The point of this article is that from a physical perspective, there is no reason to believe that the laws of thermodynamics exist. But there are less complicated examples as well.

For instance, if you have an electron placed some distance away from another negative charge source, you could very easily model its dynamics. But there is no fundamental difference between this electron being repelled from the other negative charge compared to a positron that is being attracted to the charge, but moving backwards relative to our perception of time. So it is a forward moving electron or a time-backwards positron? There's no difference, they're both completely physical systems.

Boltzmann's big accomplishment, one that was at his time rejected until Einstein's description of Brownian motion, was his completion of the H-theorem (which Claude Shannon subsequently named his information-theoretical counterpart for), which describes that physical systems under very simple assumptions (uncorrelated position and momentum vectors) will 'relax' to a distribution of energies given by the maxwell-boltzmann distribution. It turns out, however, that these assumptions are not completely valid for physical systems, so the H-theorem is not really considered a 'true' explanation. I highly suggest reading the wikipedia article on Boltzmann's H-theorem that goes into the mathematical derivation of the positive-definite nature of time derivative of entropy of a closed system.

<wild speculation> So what are the real answers as to the arrow of time? It's an unsolved problem, but I have guesses. The most obvious answer for things like this is based on the anthropic principle. In an informational world, one could assume that everything that we interact with all moves in the same time direction because DNA is effectively some Turing-equivalent string of 1s and 0s that is modified by the 'computation' of evolution. Memory of the timeline is encoded into DNA, which is what we are from an information perspective.

Chances are, however, that things like this will never be proven, possibly because in this case the proof will be non-computable by Turing machines like us. It isn't even unreasonable to think that the 2nd law of thermodynamics and P!=NP are not equivalent statements and equally unprovable. Am I far out there enough yet? </speculation>