I want to know this out of curiosity

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    $\begingroup$ I think you mean, "When you flip a mirror upside down Why doesn't the image in the mirror flip upside down too?". Because clearly, you can flip a mirror upside down. $\endgroup$ – Brionius Sep 18 '15 at 17:50
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    $\begingroup$ I flipped my mirror upside-down and now i'm staring at a panel of wood. $\endgroup$ – KutuluMike Sep 18 '15 at 17:55
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    $\begingroup$ @MikeEdenfield: It's not the mirror's fault that someone put paint and a wooden board on the back. $\endgroup$ – CuriousOne Sep 18 '15 at 17:58
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    $\begingroup$ Possible duplicate or otherwise very related: physics.stackexchange.com/q/8227/17609 $\endgroup$ – Řídící Sep 18 '15 at 18:17
  • $\begingroup$ I think this not a bad question that it got three downvotes. But it probably belong more in the math.stackexchange being about the nature of symmetry. $\endgroup$ – user16035 Sep 18 '15 at 19:26

Forget "up" and "down". The laws of physics doesn't care about orientation.

Why does it "seem" that mirrors flip L and R? Your body has a mirror plane along the Z axis. When you rotate about your Z axis you almost look the same as if you're seeing yourself in the mirror. The differences are seen with your hands who have changed handeness (the actual technical term).

Note, if you rotated about your Y axis and did a hand stand you wouldn't be concerned about your feet being where your head was because your head and feet don't look alike.

So mirrors can't "flip it" side ways either, it just seems that way. Nor is it precise that the mirror "inverts" left and right. Instead it preforms an symmetry operation called, mirror. When you turn around 180 degrees, you're preforming another symmetry operation called... rotation (very clever naming. It's also known as a two-fold rotation). There is nothing inherently more correct about a rotation vs. mirror symmetry.

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    $\begingroup$ Re a symmetry operation called "mirror" A good armchair-sciencey way of explaining it is to say, a mirror doesn't reverse "left" and "right", it reverses "front" and "back". $\endgroup$ – Solomon Slow Sep 18 '15 at 19:36
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    $\begingroup$ The front/back thing is how I always thought of it. Like scaling the world by a factor of -1 along the z-axis into the mirror. $\endgroup$ – MichaelS Sep 18 '15 at 19:45
  • $\begingroup$ I was going to use the word projection, which is how I thought of it, but decided against it. It's a tough Q to answer! $\endgroup$ – user16035 Sep 20 '15 at 12:38
  • $\begingroup$ The actual term is "handedness"... $\endgroup$ – user21820 Jan 25 '17 at 4:23

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