Time Reversal

In physics, time reversal refers to a theoretical scenario where the direction of time is reversed, thus reflecting the system's evolution backward. Here are some key insights from experts on this concept:

1. Basic Principle:

   • According to Sean Carroll, time reversal involves creating a state where all momenta are reversed while keeping positions the same. When you evolve this state backward in time, and then reverse the momenta again, you get back to your initial state. This process preserves information over time in microphysical dynamics, such as those governed by Newtonian, Hamiltonian, or Schrödinger equations 1.

2. Reversibility vs. Symmetry:

   • Time reversal symmetry means that the laws of physics work the same way whether time progresses forward or backward. In classical mechanics, this involves reversing momenta. In quantum mechanics, it requires taking the complex conjugate of the wave function. Time reversal invariance ensures that evolving a system forward, applying a time reversal operation, evolving backward, and applying time reversal again brings the system back to its original state 2 3 4.

     Time Reversibility

     Sean Carroll

     Sean explains the concept of time reversibility in physics, emphasizing how information is preserved over time in microphysical dynamics. He delves into the difference between macrophysical and microphysical dynamics, highlighting the role of the past hypothesis in connecting the two realms.

     

     Mindscape Podcast

     Mindscape Ask Me Anything, Sean Carroll | April 2022

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3. Macrophysical Dynamics:

   • While microphysical laws are time reversible, macrophysical dynamics, like a glass of water warming or cooling, aren't. For instance, if you see a glass of cool water, you can't tell if it was warm water with an ice cube, because the macro state doesn't contain enough information to distinguish between the two scenarios without knowing all micro details 1.

4. Black Holes and White Holes:

   • Carroll likens black holes to melting ice cubes, where the formation of a black hole increases entropy. Although the underlying laws are time reversible, crossing the event horizon of a black hole isn't symmetric. However, a white hole, the time-reversed counterpart of a black hole, can theoretically allow particles to exit but not enter, maintaining the symmetry 5.

5. Violations and Symmetry:

   • Time reversal symmetry is not always preserved in physical laws, as demonstrated by weak interactions in particle physics. This necessitates the use of CPT symmetry (Charge, Parity, and Time), which combines these three symmetries to maintain laws of physics across different conditions. This broader symmetry helps reconcile time symmetry violations seen in experiments 2 4.

6. Fundamentals and Emergence:

   • Carroll discusses that the direction of time in physics doesn't inherently have directionality, as time is just a coordinate. Hamiltonian mechanics illustrates how momentum is fundamental and can be reversed to simulate time reversal. The principle of increasing entropy from low entropy states (like the Big Bang) gives the macroscopic arrow of time its direction 6 3.

Understanding time reversal provides deep insights into the foundations of both classical and quantum mechanics, highlighting the difference between theoretical time symmetry and observable realities.