# Mirror image inversion in the 4th dimension.

jbriggs444
Homework Helper
2019 Award
But from the perspective of your family, you are the one who has been flipped. Weird right?
Not any weirder than looking out the train window and thinking that it could just as well be the landscape moving past. The unexpected bit is finding that there actually is an experimental test that can detect chirality reversal.

BruceW
Homework Helper
So let's move up by one dimension of Euclidean space.

Now you are analogous to Pancake Man. A 4-D creature picks you up and flips you. But not your room.

From your POV, your room has been flipped. It now looks like a mirror image of it's original self.

But from the perspective of your family, you are the one who has been flipped. Weird right?
yeah, sounds about right. It is pretty weird. And you wouldn't be able to read any of the writing on the walls of your room, because it would get reversed! You'd have to learn to read and write in the opposite way!

yeah, sounds about right. It is pretty weird. And you wouldn't be able to read any of the writing on the walls of your room, because it would get reversed! You'd have to learn to read and write in the opposite way!
Yes! And Burger mentioned some funny things, for instance such a creature could turn a left shoe into a right shoe.

And if it did that with an electromagnet, it would violate the laws of physics.

Not any weirder than looking out the train window and thinking that it could just as well be the landscape moving past. The unexpected bit is finding that there actually is an experimental test that can detect chirality reversal.
Let's say your family came back and saw that the tattoo on your right arm is now on your left, that would be really unexpected. :tongue2:

BruceW
Homework Helper
also, there are biological molecules which occur mostly in one 'handedness'. So if you got flipped, while the rest of the world remained the same, then the biological molecules in the rest of the world would be the wrong way around! This might mean that you couldn't digest any food, e.t.c. I don't know much biology, so I am not certain, but it seems like you would have a hard time surviving in a world which you a 'flipped' relative to!

also, there are biological molecules which occur mostly in one 'handedness'. So if you got flipped, while the rest of the world remained the same, then the biological molecules in the rest of the world would be the wrong way around! This might mean that you couldn't digest any food, e.t.c. I don't know much biology, so I am not certain, but it seems like you would have a hard time surviving in a world which you a 'flipped' relative to!
You'd beg the 4-D creature to flip you back. :yuck:

also, there are biological molecules which occur mostly in one 'handedness'. So if you got flipped, while the rest of the world remained the same, then the biological molecules in the rest of the world would be the wrong way around! This might mean that you couldn't digest any food, e.t.c. I don't know much biology, so I am not certain, but it seems like you would have a hard time surviving in a world which you a 'flipped' relative to!
our enzymes aren't symmetrical right? :tongue2:

DEvens
Gold Member
err. maybe think about what happens to a 2d person, when we reflect him through our 3rd dimension. his right hand becomes his left, and his right eye becomes his left, so from his perspective, he looks the same. Also, his (2d) room flips in a similar way, so from his perspective, the room looks the same as well.

So in conclusion, everything should appear to stay the same?
That's not how reflection in a mirror works.

If you stand in front of a mirror and raise your right hand, your image in the mirror raises the hand on the same side. Do you have a ring on that hand (or are lopsided) then you see the ring hand being raised. Lie down in front of the mirror, your top (now, say, your right hand side) is your image's top. Raise your top hand and your image raises the same hand.

What is reversed is depth. As you approach the mirror, moving "north" say, your image gets closer to the front of the mirror but from the other side. Your image is moving "south," just the opposite. Similarly everything in the room with you.

Or to put it another way:

^
| y-axis on real side
|
|_______> x-axis on real side

===================== mirror

_______> x-axis on image side
|
| y-axis on image side
|
v

The x-axis is imaged pointing the same way. The y-axis is imaged reversed.
Dan

BruceW
Homework Helper
I don't understand what you are disagreeing with. I agree with what you are saying. When we do a reflection, the person's right hand gets mapped to his left hand and his right eye to his left eye. That is what I meant. In your example, we replace y with -y and x stays the same. So the point that was his right hand becomes his left hand

I don't understand what you are disagreeing with. I agree with what you are saying. When we do a reflection, the person's right hand gets mapped to his left hand and his right eye to his left eye. That is what I meant. In your example, we replace y with -y and x stays the same. So the point that was his right hand becomes his left hand
yup.

It is relative. If I were to be flipped in 4D into a mirror image of myself: 1) I would remain unchanged to myself, but it would appear that the world was backwards. 2) Anyone observing me would see me turned into a mirror image of who I once was.

Not any weirder than looking out the train window and thinking that it could just as well be the landscape moving past. The unexpected bit is finding that there actually is an experimental test that can detect chirality reversal.
The concept of relative motion is easy to grasp, but relative chirality? That's mind-blowing.