“Do not try and solve the paradox; that’s impossible. Instead, only try to realize the truth… there is no paradox.”*
Why is there a difference between past and future?
The laws of Newton are symmetrical in time while the entropy of a closed system always increases – creating an arrow of time. How can it be that the laws describing particles are the same whether we go forward or backwards in time, while a law describing the same system macroscopically is very different in terms of past and future?
Probability
Traditionally, the issue is specified in terms of probability: if we have a box with gas in it, the probability of gas particles bumping in to each other is larger in regions in the box where the density of particles is higher, so the gas particles will spread evenly throughout the box. Like the gas, any physical system in nature has a natural tendency towards maximum chaos – maximum entropy. [Read this blogpost about Carlo Rovelli’s explanation of time’s arrow emerging from thermodynamics.]
So we can now ask a more specific question: why is it that the laws of motion are symmetric in time, while entropy increase is asymmetrical (since entropy increases as time progresses)?
Time itself is asymmetrical
The paradox disappears when we realize that the laws of motion are only a partial description of the world around us. For example, when a number of billiard balls are moving around on a table, the laws of motion themselves** aren’t enough to predict what happens next – they don’t tell us where the balls will be in the next moment.
To make predictions, we need something besides the laws. The laws tell us where the balls will go given that they start in certain positions with a certain velocity, but without these initial conditions the laws of motion can’t predict anything at all.
Only if we know the positions and velocities of the billiard balls at some point in time can we can we use the laws of motion to make predictions about future positions and velocities.
Paradox Lost
The issue is not that symmetrical laws lead to an asymmetrical time-arrow; symmetrical laws in combination with certain boundary conditions lead to an asymmetrical arrow of time. But that’s not a mystery if the asymmetry in the arrow of time was already there in the boundary conditions.
*) This quote is loosely based on a scene from the movie classic The Matrix (1999) which goes: “Do not try and bend the spoon; that’s impossible. Instead, only try to realize the truth… there is no spoon. Then you’ll see that it is not the spoon that bends; it is only yourself.” For me, this movie has special meaning not only because of its philosophical content, but also because it came out in the same year in which I was diagnosed with a brain tumor.
**) The laws of motion considered here are Newton’s three laws (the law of inertia, F=ma, and action=-reaction).
This post was inspired by a discussion with Philip Rey which may be found at the bottom of this post about quantum theory, free will, and justice.
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