Time-Reversal Symmetry Explained

[fricke]

I completely have no idea what time-reversal mean.
Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry?
Also, what does that 'symmetry' mean there? An even function?

 

[lightarrow]

I completely have no idea what time-reversal mean.
Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry?
Also, what does that 'symmetry' mean there? An even function?

http://math.ucr.edu/home/baez/time/

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lightarrow

 

[Heinera]

I completely have no idea what time-reversal mean.
Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry?
Also, what does that 'symmetry' mean there? An even function?

Time reversal symmetry means that the physical laws governing a dynamical system would be equally descriptive if that system was played in reverse. For instance, if you showed a movie of the motion of the planets in some solar system to a physicist, and then showed the same movie in reverse, it would be impossible for her/him to decide which of the movies was played forwards and which was played backwards, because both would be equally consistent with Newton's equations.