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Isn't there no "proof" within the laws of physics for the second law? - you must posit a "Past Hypothesis".

by meroes 5y ago

sharpneli 5y ago
Depends on what level. Historically it was an empirical observation that was taken in as an axiom to classical thermodynamics. So it couldn't be derived from other laws. If we move to statistical mechanics we can derive the second law from probabilities. In essence it is possible for any system to break it, it's just very very improbable. Just like if you toss a coin billions of times. It's possible for you to get more, or less, than half of the tosses to be heads. It's just very very improbable to get anything more than very tiny deviations.
- meroes 5y ago
  But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. The laws of physics themsleves are totally symmetric (CPT theorem), and it is not thought the t-asymmetry of the weak interaction is responsible for the global macroscopic arrow of time. So without some statement of initial/prior conditions, we have no reason to see just the "forward" arrow unless we say something about initial/prior conditions. (Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox)
contravariant 5y ago
You can prove it in the context of Ergodic theory. Though that's a model so assuming that it correctly approximates the real world is still an assumption.
- meroes 5y ago
  Are you sure Ergodic theory does the trick? When I hear people like David Albert or Sean Carroll speak, they always make clear you need some kind of initial/prior conditions or else stat mech does not guarantee why we only see the forward arrow of time. If we assume we can reduce all physical process to the behavior of fundamental particles (or fields), and the physical laws that describe the microscopic world are entirely symmetrical (CPT theorem), you get Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox. They say the Past Hypothesis (low entropy big bang prior condition) is necessary to resolve it. *And the t-assymetry of the weak interaction isn't the reason according to the wikipedia article on time asymmetry - you still need initial conditions. "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe. "
  - contravariant 5y ago
    Well it doesn't tell you why the original state of the universe had such a low entropy, but it can at least be used to show that entropy should increase from there.

Isn't there no "proof" within the laws of physics for the second law? - you must posit a "Past Hypothesis".

by meroes 5y ago

Isn't there no "proof" within the laws of physics for the second law? - you must posit a "Past Hypothesis".

Depends on what level. Historically it was an empirical observation that was taken in as an axiom to classical thermodynamics. So it couldn't be derived from other laws. If we move to statistical mechanics we can derive the second law from probabilities. In essence it is possible for any system to break it, it's just very very improbable. Just like if you toss a coin billions of times. It's possible for you to get more, or less, than half of the tosses to be heads. It's just very very improbable to get anything more than very tiny deviations.

meroes 5y ago
But when we apply statistical mechanics to "microscopic" arrangments like a few particles in an idealized rigid box or in a vacuum, there is no arrow of time. The laws of physics themsleves are totally symmetric (CPT theorem), and it is not thought the t-asymmetry of the weak interaction is responsible for the global macroscopic arrow of time. So without some statement of initial/prior conditions, we have no reason to see just the "forward" arrow unless we say something about initial/prior conditions. (Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox)

contravariant 5y ago

You can prove it in the context of Ergodic theory. Though that's a model so assuming that it correctly approximates the real world is still an assumption.

meroes 5y ago
Are you sure Ergodic theory does the trick? When I hear people like David Albert or Sean Carroll speak, they always make clear you need some kind of initial/prior conditions or else stat mech does not guarantee why we only see the forward arrow of time. If we assume we can reduce all physical process to the behavior of fundamental particles (or fields), and the physical laws that describe the microscopic world are entirely symmetrical (CPT theorem), you get Loschmidt's Paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox. They say the Past Hypothesis (low entropy big bang prior condition) is necessary to resolve it. *And the t-assymetry of the weak interaction isn't the reason according to the wikipedia article on time asymmetry - you still need initial conditions. "Time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe. "
- contravariant 5y ago
  Well it doesn't tell you why the original state of the universe had such a low entropy, but it can at least be used to show that entropy should increase from there.