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The Arrow of Time by Robert Nemiroff Michigan Tech Physics X: About This Course • Officially "Extraordinary Concepts in Physics" • Being taught for credit at Michigan Tech o Light on math, heavy on concepts o Anyone anywhere is welcome • No textbook required o Wikipedia, web links, and lectures only o Find all the lectures with Google at: "Starship Asterisk" then "Physics X" o http://bb.nightskylive.net/asterisk/viewforum.php?f=39 Arrow of Time You look at a movie of two particles colliding. Two particles go in, and two go out. Is it possible to tell whether this movie is being shown forward or backward in time? 1. No, the movie would look normal either way. 2. Yes, the movie run backwards would look strange. 3. We did this once in elementary school and everyone laughed. Arrow of Time 1. No, the movie would look normal either way. Microphysics, involving individual interactions, is time reversible. All microphysics equations are valid when substituting "-t" in for "t". It is not possible to tell the direction of an "arrow of time" from seeing two particles collide. A key is the conservation of mechanical energy. According to Noether's theorem, systems that conserve mechanical energy are time invariant. Arrow of Time You look at a movie of a ball rolling down a hill. The ball starts from rest and increases in speed. Can you tell from this movie which direction time is running? 1. No, the movie would look normal even if run backwards. 2. Yes, the movie run backwards would look strange because balls don't roll up hills. 3. Time doesn't run. People run. That's makes all the difference. Arrow of Time 1. No, the movie would look normal even if run backwards. How can this be -- balls can't roll up a hill! But they can. Consider that after a ball rolls down a hill, it rolls UP the next hill. Consider seeing only the last part of that movie. It would seem normal. So one can't tell the "arrow of time" even using simple gravitational systems. Arrow of Time Why can't we remember the future? Psychics and physicists spend efforts trying to predict the future. Physicists are usually more accurate. No repeatable experiment has ever shown that anybody or anything has the ability to "remember" the future. It is not known why! Arrow of Time: Entropy You see a movie of an egg rolling off a table and cracking open on the floor. Would you be able to discern an "arrow of time" by comparing this movie with the same movie run backwards? 1. Yes, duh. 2. No, double duh. 3. Only if the anti-egg is unitarily cross-temporal. Arrow of Time: Entropy 1. Yes, duh. A broken egg is arguably in a higher entropy state than a whole egg. In other words, there are many more ways an egg can be broken than the egg can remain unbroken. The second law of thermodynamics says that for closed systems, entropy must increase (on the average). So the arrow of time points from the unbroken egg to the broken egg, and we know which way the movie must run to appear normal. Arrow of Time Physical processes that might define an arrow of time: • • • • • • • thermodynamics and entropy cosmology and universe expansion radiation and a stone in a pond cause and effect weak nuclear force and kaon decay quantum mechanics and wave function collapse psychological and memory Arrow of Time: Cosmology The expansion of the universe defines and arrow of time. In the present epoch, the future can be discerned from the past since the universe expands in the future. Some feel this is tied into the entropic arrow, as the universe's entropy increases with the expansion. It has been suggested that were a closed universe start to re-contract, the arrow of time would reverse, so that it is impossible for us to experience a Big Crunch. Arrow of Time: Causality Watching cause and effect might define an arrow of time. Some feel this is a result of the entropic arrow of time, since on the average, the effects of a cause will be known statistically only because they have higher entropy. Arrow of Time: Weak Particle Decay The weak nuclear force admits interactions that are not, on the average, symmetric in time. They are also not left-right symmetric in time, so that separated observers could establish left and right without knowing each other's prior orientation. This process is thought responsible for why there is more matter than antimatter in our universe. The kaon exhibits such an asymmetric decay. Still, many such decays must be seen to discern a time arrow. Arrow of Time: Quantum wave collapse The act of measuring a particle, according to the Copenhagen interpretation of quantum mechanics, is not a time-reversible process. Therefore, we can orient an arrow of time to point in the direction of wave functions collapsing. Recent work on quantum decoherence, however, indicates that wave function collapse might (also) be related to the entropic arrow of time.