Time Reversal Symmetry


Time reversal symmetry demonstrated by Bach's Crab Canon in Musikalisches Opfer (1747):

Music score of Bach's crab canon


The music score can be played backward, starting from the end and ending at the beginning, and should sound exactly the same as the original score. This music is composed with the "retrograde inversion" technique, where the left hand plays the music score of the right hand in the backward procession. This high degree of symmetry makes the music sounds extremely harmonious. Here is a youtube video to visualize the music progression.


Recording of the music plays forward (on a piano):

Audio file

The same recorded music, now plays backward in time:

Audio file


Do the two pieces of music sound the same?


If they don't sound the same to your ears, then it shows the time-reversal symmetry is broken!


But how?


If you figured out how the time-reversal symmetry is broken in Bach's music, send me a short message explaining your reasonings.