In Good and Real, Gary Drescher uses the example of a simulated space in which there are large fast-moving balls and small slow-moving balls. Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time’s arrow. How? By noticing that the large balls leave wakes behind them: paths that are cleared of small balls by the passage of a large ball. If you run the movie forwards, the large ball pushes small balls out of the way and leaves a wake; if you run the movie backwards, empty paths clear out in anticipation of a large ball coming through, and small balls fill in behind it.
In other words, even though a single collision is time-symmetric, the development of the whole simulation is asymmetric, because the distribution of small balls at any moment is correlated with where the large balls have been but uncorrelated with where they are going next.
Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time’s arrow.
I haven’t read Drescher’s book, but this sounds like the usual Boltzmann-style attempt to explain the arrow of time by starting in a low-entropy state. When you start with many small balls, all moving at similar (because small) velocities, you are in a low entropy state. As the clock advances, you wander from this highly atypical low-entropy region of configuration space into more typical high-entropy regions. This is what gives you all sorts of time-arrows, such as the tracks left by the big balls.
The problem with using this as a global arrow of time is that, if you run the simulation backwards from the initial low-entropy state, you will again almost surely wander into a high-entropy state. From the point in time when entropy is minimized, both directions in time will look like futures (almost surely).
Imagine that you start with a big 2D box. Assume that all collisions are elastic. In the initial configuration, the box is evenly filled with a bunch of nearly-stationary little balls, and one big ball with large initial velocity. As you run the simulation forwards, you’ll see the big ball clear out a path behind itself as it moves through the little balls, just as you said.
But now run the simulation backwards from that same initial configuration. You’ll see exactly the same time-arrow-indicating phenomena as the simulation runs backwards. Only now, the time-arrows will be pointing into the past (towards which the simulation is running).
After running the simulation backwards for a while, stop, and rerun the simulation forwards from that time in the past. It will seem uncanny as the balls arrange themselves just so, but something strange had to happen for the balls to end up in the wildly improbable initial configuration with which we began.
Drescher actually deals with this — from an initial configuration, positive or negative movement both work as time arrows; time can be measured as distance in accumulated correlation from that initial state in any particular direction. At zero, moving along the positive or negative direction is equally “forward in time”; but at +42, it isn’t.
Viewed from a very local level (encompassing just a single collision), there’s no arrow of time, because entropy doesn’t change significantly.
Taking a middle-level view (encompassing more balls for a greater span of time), there’s a unique time arrow as you pass from the low-entropy initial configuration to a higher one.
But taking a global view, encompassing all balls for all time, you lose the unique arrow of time again, because you are just as likely to leave low-entropy states as time runs “backwards” as you are when time runs “forwards”.
In other words, even though a single collision is time-symmetric, the development of the whole simulation is asymmetric, because the distribution of small balls at any moment is correlated with where the large balls have been but uncorrelated with where they are going next.
It would be fascinating to observe an instance of this universe that was symmetric. It is certainly possible. With the right starting conditions you could have a universe that runs forward but looks like it is being played backward. With another set of starting conditions a universe could be found that looks just as plausible running forward as backwards.
It would be fascinating to observe an instance of this universe that was symmetric. It is certainly possible. With the right starting conditions you could have a universe that runs forward but looks like it is being played backward.
In Good and Real, Gary Drescher uses the example of a simulated space in which there are large fast-moving balls and small slow-moving balls. Locally, the physics of collision are time-symmetric; if you observe a movie of a collision between just two balls, you cannot tell if the movie is being played forwards or backwards in time.
However, when you look at a movie of the whole simulation, you can easily identify the direction of time’s arrow. How? By noticing that the large balls leave wakes behind them: paths that are cleared of small balls by the passage of a large ball. If you run the movie forwards, the large ball pushes small balls out of the way and leaves a wake; if you run the movie backwards, empty paths clear out in anticipation of a large ball coming through, and small balls fill in behind it.
In other words, even though a single collision is time-symmetric, the development of the whole simulation is asymmetric, because the distribution of small balls at any moment is correlated with where the large balls have been but uncorrelated with where they are going next.
I haven’t read Drescher’s book, but this sounds like the usual Boltzmann-style attempt to explain the arrow of time by starting in a low-entropy state. When you start with many small balls, all moving at similar (because small) velocities, you are in a low entropy state. As the clock advances, you wander from this highly atypical low-entropy region of configuration space into more typical high-entropy regions. This is what gives you all sorts of time-arrows, such as the tracks left by the big balls.
The problem with using this as a global arrow of time is that, if you run the simulation backwards from the initial low-entropy state, you will again almost surely wander into a high-entropy state. From the point in time when entropy is minimized, both directions in time will look like futures (almost surely).
Imagine that you start with a big 2D box. Assume that all collisions are elastic. In the initial configuration, the box is evenly filled with a bunch of nearly-stationary little balls, and one big ball with large initial velocity. As you run the simulation forwards, you’ll see the big ball clear out a path behind itself as it moves through the little balls, just as you said.
But now run the simulation backwards from that same initial configuration. You’ll see exactly the same time-arrow-indicating phenomena as the simulation runs backwards. Only now, the time-arrows will be pointing into the past (towards which the simulation is running).
After running the simulation backwards for a while, stop, and rerun the simulation forwards from that time in the past. It will seem uncanny as the balls arrange themselves just so, but something strange had to happen for the balls to end up in the wildly improbable initial configuration with which we began.
Drescher actually deals with this — from an initial configuration, positive or negative movement both work as time arrows; time can be measured as distance in accumulated correlation from that initial state in any particular direction. At zero, moving along the positive or negative direction is equally “forward in time”; but at +42, it isn’t.
Oh, okay. Then Drescher has it right:
Viewed from a very local level (encompassing just a single collision), there’s no arrow of time, because entropy doesn’t change significantly.
Taking a middle-level view (encompassing more balls for a greater span of time), there’s a unique time arrow as you pass from the low-entropy initial configuration to a higher one.
But taking a global view, encompassing all balls for all time, you lose the unique arrow of time again, because you are just as likely to leave low-entropy states as time runs “backwards” as you are when time runs “forwards”.
It would be fascinating to observe an instance of this universe that was symmetric. It is certainly possible. With the right starting conditions you could have a universe that runs forward but looks like it is being played backward. With another set of starting conditions a universe could be found that looks just as plausible running forward as backwards.
I describe such an instance here.