1
$\begingroup$

I often hear that on the microscopic level, time-reversal symmetry is true for all physical processes. However, I can easily come up with counterexamples that seem to disprove this:

  • Two particles of opposite charge being attracted by each other and accelerating towards one other as a result.

Furthermore, even barely observed on a microscopic level, the gravitational force surely defies time-reversal symmetry. A movie of an apple accelerating away from the ground is immediately recognizable as the reversed version of the true process. This is a macroscopic example, but you get the point.

So where am I wrong?

$\endgroup$
  • 2
    $\begingroup$ Assume CPT symmetry and since CP violation is observed, T symmetry is also violated. (my limited knowledge in particle physics) $\endgroup$ – K_inverse Dec 3 '18 at 12:28
  • 2
    $\begingroup$ Unless the two particles of opposite charge smash together into one, they fly towards each other, undergo Rutherford scattering, and fly apart in a way that is indistinguishable from them flying towards each other - your counterexample isn't a counterexample at all. $\endgroup$ – Jon Custer Dec 3 '18 at 13:47
2
$\begingroup$

Furthermore, even barely observed on a microscopic level, the gravitational force surely defies time-reversal symmetry. A movie of an apple accelerating away from the ground is immediately recognizable as the reversed version of the true process.

No. When an apple falls from a tree, it starts motionless at a high point, then gains more and more speed as it moves lower. The time reverse of this occurs when you throw an apple up. It starts with high speed at the bottom, then ends up motionless at a high point. In both cases the acceleration is toward the ground.

More mathematically, suppose the position of the falling apple is $y(t)$. Then the acceleration must be $-g$. When you time reverse the trajectory to get $y(-t)$, you get two minus signs when differentiating from the chain rule, so the acceleration is still $-g$. So if $y(t)$ is a legal path, so is $y(-t)$.

You might say the time reversed process is impossible, because obviously an apple can't jump up from the ground and back into the tree. But that's the entire point of the paradox. Microscopically, Newton's laws allow both processes; it's only thermodynamics that forbids one.

$\endgroup$
  • $\begingroup$ To expand: time reversal states that in a field of forces (e.g. graviy of electric field), which for simplicity we require to be conservative, if a motion from point r(0) with velocity v(0) leads, after a time t, to the new point r(t), v(t), then a hypothetical motion starting at r(t) with velocity -v(t) goes "back" to r(0), -v(0) and it does so along the same path. As knzhou wrote, that means, you can't tell the difference from an apple been thrown up and a falling apple with time flowing backwards. They look the same. But one occurs spontaneously in the macroscopic world... $\endgroup$ – JalfredP Dec 3 '18 at 12:37
  • $\begingroup$ @JalfredP there has to be energy conservation, if energy is provided , the mathematical path will be the same. In short "given the initial +endpoint fourvectors and the field, the path is the same" $\endgroup$ – anna v Dec 3 '18 at 13:07
  • $\begingroup$ I did say "conservative field" i.e. energy is conserved and the path is well defined (: $\endgroup$ – JalfredP Dec 3 '18 at 17:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.