# Physics of time running backwards

Although it would seem weird to analyze physical phenomena when time runs backwards, it seems to have a logical sense, at least for me:

• Entropy would tend to decrease: two balls having energy interacting would cause one of them (the one having the highest amount of energy) to collect all energy; in fact, as far as I see, thermodynamics laws would hold, except that the second law will be reversed (so, the interpretation would be that energy tends to concentrate, instead of spreading);
• Force fields would just change direction; attractive entities will repel and vice versa; anodes will have the effect of cathodes, etc.
• What we call "input" of a system would just act in a reverse direction; so, causality would just be reverted (at least, at a linguistic level).
• The relationship between kinetic energy and potential energy would be reversed!! (if I'm not wrong, energy types regarding time can possibly be interpreted as: potential energy is change to happen in the future; kinetic is change that happened in the past).
• etc.

Is there any formal study/book addressing the subject of backwards-time physics (also called retro causality) (I just find speculations and scarce punctual observations)?

• In quantum mechanics there is a time-reversal operator. You can use this operator to study how other operators change under time reversal, for example $\hat{\mathbf{r}}$ remains the same, but $\hat{\mathbf{p}}$ is reversed. Commented Feb 23, 2019 at 11:53

Yes, we talk about T-symmetry or time reversal symmetry when physical laws under the transformation of time reversal remain the constant. In quantum mechanics a time-reversal operator $$\hat{\Theta}$$ can be defined. You can use the properties of this operator to study how other operators change under time reversal, for example $$\hat{\mathbf{r}}$$ remains the same, but $$\hat{\mathbf{p}}$$ is reversed. Modern Quantum Mechanics by Sakurai deals with this topic in chater four.

Some of the assumptions you made are incorrect, for example forces will remain the same. Dimensionally speaking $$F=MLT^{-2}$$, so time reversal won't affect the direction of the force. Imagine a cassical electron orbiting a nucleus, under time reversal the electron's velocity is reversed, but the force between the eletron and the nucleus is still attractive.