[Physics] Where does the irreversiblity came from if all the fundamental interaction are reversible?

arrow-of-timeentropyinteractionsreversibilitystatistical mechanics

There isn't too much to explain:

We know that all fundamental forces are reversible then where does the irreversibility come from?


Edit: The following is edit based on comments:

Consider a block of wood and you just make it slide on a desk, it will move a little bit and then stop. It stops because of molecular forces as surfaces are rough, of course, they aren't uniform surfaces at all. And then bonds break so we say that friction is at the molecular level. So if we need quantum mechanics for explaining these things but apart from that, We know that friction that makes the block stop is at the molecular level. This means, that energy can transfer from one system to another at the molecular level. These are random motions and that is even though all forces are conservative at the fundamental level, it may turn out that energy can dissipate as heat, which we can't recover.

I'm asking what's the origin of this macroscopic irreversibility, Why we can't recover the energy which gets lost if at the fundamental level these forces are reversible?


Stating from Wikipedia,

Time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal,
$T:t\rightarrow -t$

Stating R. Shankar, "You will no way of knowing if the projector is running forwards or backward."

Further Stating Wikipedia,

Since the second law of thermodynamics states that entropy increases as time flow toward the future, in general, the macroscopic universe does not show symmetry under time reversal.

Now consider that I'm studying the microscopic universe, So I would expect time-reversal symmetry. (We can't tell if the picture running forward or backward). Now lets I start adding more elementary particles in my system, When does it so happen that I can tell that this picture is actually running forward.

Best Answer

There's a distinction between microscopic reversibility and macroscopic reversibility. Or if you will, a difference between something being irreversible in theory versus irreversible in practice. (Or absolutely irreversible versus probabilistically irreversible.)

A hopefully relatable analogy:

Imagine that you have a large number of coins in front of you. They all start heads-up (obverse visible). Now imagine that at each "step" you choose a coin randomly and flip it. That is, if it's heads-up, you make it heads-down, and if it's heads-down you make it heads-up. Each step is reversible. If you flip a coin heads-down in one step, you can flip it heads-up in the next. But actually running the experiment will accord with your (likely) intuition -- if you choose coins at random, the coins become a random (approximately equal) distribution of heads-up and heads-down. Even though each individual step is reversible, on the macroscopic scale the combination of steps is not: if you start with an all heads-up state, you never go back to that same state.

Theoretically, you could. It's possible that you just so happen to randomly get a streak where you pick only those coins which are heads-down, and flip them heads-up. Or vice versa: only select heads-up coins and flip them heads-down. But since you're picking randomly, that's a very, very low probability case. And it gets even less probable the more coins you have to flip.


Physics systems are similar. Most macroscopic systems are composed of a large number of individual particles/elements. While the individual interactions of the particles are reversible (like the individual coin flips), on a global, macroscopic scale the system isn't. Indeed, all of those interactions could theoretically run in just the right way to revert the system to exactly the previous state, but the probabilities of that are small. You could be talking about $10^{20}$ or $10^{30}$ particles, each of which need to be properly reversed. While the chance of any individual interaction being reversed could be quite high, the chance that all of the interactions are reversed in just the right way to put the macroscopic system back into a previous state is mind-bogglingly low.

There's different formulations of entropy, but in many that's what entropy is -- it's the measure of the "probability" of the state (Boltzmann's entropy formula). When someone says that things proceed from low entropy states to high entropy states, they're basically saying that things proceed from a low probability states to higher probability states. But the second law of thermodynamics is a statistical one, not an absolute one. "Entropy always increases" is of a slightly different character than "energy cannot be created or destroyed". It's not a hard-and-fast rule which can never be broken, it's just $10^{20}$ to 1 odds that it won't be.

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