Post YOUR Answer Here

[MikeO]

Please post your answer here and we can discuss it.

[jclawrence]

Here's my solution. If you hold up a piece of paper with your name on it in front of a mirror, you will see on the mirror exactly what you will see looking at the piece of paper from the rear. So the mirror reflects back, point for point, exactly what's on the piece of paper. And if the paper's thin enough and the ink strong enough, you will see both on the paper and on the mirror exactly the same thing which is your name written backwards. If the mirror were a half mirror, i.e., it let half the light through, then a person standing in back of the mirror would see your name exactly as written, but a person standing in front of the mirror would see your name backwards which is how the person holding up the piece of paper would see it as light passed through the piece of paper.

[MikeO]

Howdy jclawrence.

So you're proposing to use a half silvered mirror (one that's translucent), and a translucent piece of paper.

That's an interesting variation on a theme I've seen before.

But then, how will this arraignment explain the riddle to someone looking at the same mirror, and asking you about his image being Left/Right reversed, but not Up/Down reversed?

Maybe your arraignment will cause him to say Left/Right is only half reversed, but that's still a lot more than the zero Up/Down reversedness he perceives.

[atgc]

I asked this question to a fellow physicist, and his answer was quick. The notion of left/right is distinct from the notion of up/down; one is a pseudovector, and the other is a vector.

Let me be a bit more precise. If we take 'up' to be the direction from our centre to our head, and 'front' to be the direction from our centre to our navel, then we are left with two choices for the third orthogonal direction. Having chosen one of these as "left", we now have an oriented frame attached to ourselves. Our mirror image always has the oppositely-oriented frame, regardless of how we align ourselves with a mirror. This is the left/right reversal which we observe and have difficulty coming to terms with. Until one sees that left/right are not ordinary vectors, one will not completely grasp the mirror paradox.

The unambiguous answer is that a mirror changes chirality/orientation (which is labelled left or right). Confusion arises when we think of left and right as direction vectors (like east/west), which as I stress again, is incorrect. A chirality change can manifest itself in many different ways, typically a change in the direction of one axis (this is Feynman's explanation), but this is not the only way. The coordinate-independent way to express what a mirror does is that it reverses chirality (or 'orientation' in the mathematics literature). This does not depend in any way on operational definitions, alignment of the mirror and subject etc., and is quite simply, the role of a mirror. Indeed one would not expect that the subjective views of a conscious being should alter the behaviour of a mirror.

If you look at the structure of the group of rigid motions in 3-dimensional space, there are rotations, translations and reflections. The first two are continuous, while reflections are discrete. This is the key point. We cannot transform ourselves into our mirror images in a continuous fashion. Mathematically, one says that the rigid motions are divided into two disconnected components -- roughly speaking, the continuous transformations in our world, and the continuous transformations in the mirror-reflected world. Therefore, we may try very hard to twist and turn ourselves to match with our mirror image, but this is a mathematical impossibility -- and in a sense, the source of the paradox. The deep unresolved question is really, why this mathematical disconnect seems correspond to a physical disconnect.

Therefore, I argue that our instinctive view that a left/right reversal has taken place in the mirror is correct. The paradox arises because mistakenly assumed that left/right has the same status as up/down, as direction vectors, when in fact the former are really chiral pseudovectors. In fact, we are even justified to feel aggrieved that something is amiss in a mirror -- there is just no continuous way to transform ourselves (or perhaps, even the laws of physics) into our mirror image.

[MikeO]

Howdy Guest atgc!

We're going to have to talk.

There are a lot of terms to nail down and translate here, and I'm looking forward to giving it a try.

MikeO

[MikeO]

atgc,


After a few minutes thought, I think we're probably saying the same things. This is my prediction of the scene after untangling all the terminology.

Notice how Feynman and I were saying the same things (color coded here), but we had slightly differing vocabulary.

Well, you and I, atgc, have vastly differing vocabulary, but are saying the same things IMO at this early point in the analysis.

Also, notice how Feynman and I differ in that Feynman stops short in considering the common non-physicist's hungers-to-know in his explanation.

I want to go all the way in answering the FEELING that most people get, and put into words, that mirrors SEEM TO reverse left and right but not up and down.

May I ask you, atgc, how you expect your answer to help the common non-physicist's simple daily observations in a bathroom mirror?

I'm thanking you for your answer. Would you like to help me show that there's a parallel here in your explanation and mine that rivals the parallel between Schrödinger’s waves and Heisenberg's matrices? Wow! Why, it'll be as grand as Libenitz and Newton both discovering the calculus!

Ok, it's time for me to take my grandiosity meds.

But let's talk, ok?

[MikeO]

BTW, I'm onto the labeling of left/right when it comes to the two possible Cartesian co-ordinate systems.

We might start by showing in the conventional xyz sytem (z coming out of the page) how multiplying any one axis by -1 (reversing it) produces the "mirror image" or opposite coordinate system (z going into the page).

Also note that when we talk in this math/physics arena, reversing means rotation of 180 degrees. This math/physics type of "reversal" is ISOMETRIC to the "rotations" I describe throughout this website.


***


If you and your phyicist friend could focus your terminology to the common configuration the common non-physicist sees daily: a vertically hung bathroom mirror.

Once we nail down what's going on in that up/down left/right, forward/back environment, we can extend the analysis to more complex configurations.

[MikeO]

I'm just thinking out loud. I had to do this for 5 years when I first heard the mirror riddle, waiting for my first breakthrough.

I'm now remembering working on the "chirality" thing once long ago. There's a problem with nomenclature there.

As an aside, is anyone familiar with Benjamin Franklin's UNFORTUNATE choice of "positive" and "negative" designations in static electricity generation experiments. If ONLY he had done it the other way around, lebeling them "negative" and "positive" the math would have worked MUCH NEATER.

In chirality, the lebels "left" and "right" are similarly unfortunate for this mirror configuration, because the same terms are used for a major axis in the configurations co-ordinate system, i.e., the observers "right" and "left" arms. For these purposes terms like "A" and "B," or maybe "standard" and "non-standard" are far less confusing if chirality is to be brought in.

So THAT would have to be the first thing in translating my explanation and your (atgc) explanation towards eachg other in nomenclature.

[MikeO]

I seem to be remembering that there may already be some knooks and crannies here where I already started working on this approach.

I'll have to check.

[MikeO]

Ok, I found it.

It's in the "Deep Ramifications" thread but I didn't get very far with typing it out.

I'm also suspecting that there is not only a terminology disconnect here also.

Tell me, atgc, do you think your friend was addressing the problem at hand or a slightly different one?

I suspect that your friend is NOT addressing the problem at hand which is the human FEELING that left and right are reversed. I don't think your friend is trying to explain this common human feeling.

Instead, I believe your friend is addressing a rather UNRELATED problem, that does have some similar terms and configurations. It sounds like is in some kind of math space, and not dealing with this issue.

[juan]

One thing I think might be helpful is to notice that we take reference points when we think about an axis. In the environment this is much easier to see in the vertical axis: ground-sky. That's because the Earth's surface is basically a plane of symmetry, which is the surface itself, dividing the space in which we stand into "up" (the sky-towards end of the vertical axis) and "down" (the ground-towards end of the vertical axis).
Our body also has reference points in the axis perpendicular to our transversal plane, that is, the vertical axis: head to the top, feet to the bottom. Maybe this is why people perfectly notice that there's no inversion in the vertical axis. The head is still pointing to the sky.

The coronal of frontal plane divides our body in two, front and back, and we also have points of reference in our body, as our face is only to the front, our back is only to the back, and so on. But the same doesn't happen with any part of the planet we're standind in, unless we have objects of reference. But, in general, the front-back difference is not so clear on the planet's surface, not as the ground-sky opposition (also enhanced by gravity!); we couldn't even tell where the frontal plane is (and we take the mirror as an answer). And if there's some mountain on our back that has no counterpart ahead of us.... we often look at the mirror with our front. So the mountain is also reflected, and we might think there's no front-back inversion because in the mirror's image the other self also has the mountain behind them. The remedy for this would be to think about ACTUAL mountains or any other reference, beyond the matter that composes the mirror; something that is present behind our back, and absent beyond the mirror. And then take the mirror's borders to establish the frontal plane, but using the references of the real world. I guess because of this - the mirror's most common position - people don't see the obvious inversion in the front-right axis (perpendicular to the mirror's surface, actually).

Finally, the sagital plane, the one that divides us into our left and right halves. We are, generally speaking, symetric here. Some of our internal organs aren't, but as we don't see them, they don't change this fact. Mammals have bilateral symetry, that is, tissues develop with the same pattern each side of the sagital plane. In Anatomy we talk about inner-outer, more than left-right, precisely because of this symmetry: "inner" means closer to the body's midline, and "outer" means further away from it. In a way, Anatomy studies half bodies, with absolute references for the axis perpendicular to the transversal plane: inner (towards the vertebrae) and outer (towards the shoulder). But, back to the entire body... we don't have some cardiac protuberance on the left of the torso, nor a liver protuberance to its right. In that case, we would easily notice the wedding ring is still towards the cardiac protuberance in the mirror image. And I can't imagine whether we would have developed the concept of right and left in the first place, if we lacked bilateral symmetry.
The planet's surface also lacks an evident opposition in the sagital plane -- moreover, there even isn't such a plane, like in the case of the frontal plane. The planet's surface is our best reference while being on the Earth, and that surface consists on a horizontal plane and basically the lack of any other, thinking of it matematically. Therefore, whith no sagital plane dividing the environment, and with no obvious visible references different on each of our body's halves (where we do have such a plane)... and with the mental concept of left and right! Our mind finds it hard to resist the temptation of using that concept.

------------------------------

Another thing, about why we tend to use the concept or left and right even more.
As it's been already discaussed, it's not the mirror but the observer who reverts the image, in their brain. And they invert the image because they RECOGNIZE holaobserver doesn't recognize as left-right oriented, something that would be interpretated the same way in any left-to-right or right-to-left orientation.
Can you read Russian? I can't. So if I happen to take a text entirely written in Russian, and then invert it horizontally, I wouldn't really notice the change. So, if texts written in Russian were the only thing I had ever seen reflected on a mirror, I wouldn't even understand what paradox people talk about.

[MikeO]

Hello jimd, and WELCOME!

I must apologize to you. I accidently deleted your post, while trying to respond with the following:

The reason I no longer follow the method you proposed here is because the answer to the mirror riddle is NOT to be found in the Physics of light rays.

The mirror reversal is something that SEEMS to happen, and therefore, is in the realm of HUMAN PERCEPTION, and not simple Physics.

Please look at the third brief answer in the thread titled "Concise Summary of the RIGHT Answer" for more on this.

[MarkJ]

I thought of using the third axis of rotation not described in your section - around the axis from the center of your body directed towards the mirror.

If you are standing upright and look at the mirror, you can be subject to the belief (depending on your point of view) that the the mirror is reversing your image from left to right.

If you rotate your body by 90 degrees around the axis from your belt buckle to the mirror, you are now lying down (like on a bed) with your face pointing towards the mirror and (as an example depending on the direction of rotation) your left hand pointing down and your right hand pointing up. When you look at the mirror, you can still convince yourself that the mirror has "reversed" your image, but now you would have to believe that the mirror has reversed it up-down since your left hand is down and your right hand is up.

Thinking about the two situations (standing up looking at a mirror and lying sideways looking at the same mirror) many of the pseudo scientific explanations melt away. If the mirror was smart enough or the optics somehow contrived to reverse an image left to right, then when you rotate your self 90 degrees so that you are lying down the "reversal" should be from your head to your feet. Since this is not how the image appears, the only conclusion is that it is your perception of the image and not the image itself which is reversed.

[MikeO]

YES!

It far more a perception thing
than an actual image revesal.

It's a people thing,
and not Physics.

[MikeO]

Thank you for those comments, juan.

I was looking at them again today.