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I have a relatively bizarre question which I'm not even fits into the category of mainstream physics, but here I go anyway.

I want to consider two hypothetical situations. Then I want to see if there is any physical means of distinguishing the two apart.

One of these scenarios involves a perfectly flat reflective surface in a particular region in space that reflects all of the incident radiation, and this surface is unable to undergo shape deformation due to forces, thermal expansion, etc. As this is merely a surface on a body, it is not possible to view the back of this reflective surface. If stationary, the mirror will produce a perfect image, as expected.

For the other scenario, consider the very same region in space. Replace the reflective surface from the first case with a finite plane. Now consider a second universe that is perfectly symmetrical to the first universe about said plane. The hypothetical rule that this second universe must follow is that it does the same, except reflected, as the first universe. Let these two universes "intersect" at the said finite plane, in such a way that looking through the plane one way allows you to view into the second universe as if looking through a mirror. Like case 1, you cannot make such an observation by look at "the back" of the intersecting plane.

So, is it possible for these two situations to be distinguished apart? What the first universe does, the second does reflected, so looking through the intersecting plane in case 2 should be identical to looking through the mirror in case 1. So, visually, the two should look the same.

If you were to try to walk through the intersecting plane (case 2), since your mirror double would be doing likewise, you and your double would end up getting in each other's way, making it the same as case 1, where the mirror would get in your way if for some reason you fancied walking into one.

If you put your hand on the intersecting plane, and your double does likewise, I doubt you would be able to feel the texture of the other hand, distinguishing it from a smooth mirror, as I believe friction between both surfaces is key for distinguishing the feeling between different materials. If the second universe reversely replicates the first universe, then both of the hands would be moving without slip, in unison, as if sliding your hand on a smooth mirror.

As for how photons act for case 2, I'm not sure as I don't know much at all in QM or relativity. If photons were to collide off each other like a macroscopic elastic collision, they would probably reflect in the same manner as a mirror. In this case, the intersecting plane acts like a proper mirror. If the photons pass through each other without colliding, then it will be as if the photons reflected, except the two photons have been swapped around. Perhaps the photons interact in a different way? I'm not sure.

What would have if the mirror/intersecting plane moved/accelerated (at high speeds) from the observer? Would differences arise due to relativistic effects?

And, for a bonus, more philosophical question, if, by the end of all reasonable observations, you are unable to distinguish the two cases, is there anything in scientific practice to justified saying that the two cases are physically identical?

Hopefully this question makes some sense. If something doesn't make sense, please let me know.

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  • $\begingroup$ I'm pretty sure you could halve this question size. $\endgroup$ – lemon Apr 10 '15 at 20:12
  • $\begingroup$ Sure, but by removing what exactly? Does it have unnecessary details, or is it too wordy? $\endgroup$ – Involutius Apr 10 '15 at 20:15
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That is interesting. At the very least, you should be able to tell the difference between the mirror and the world if you put your hand out to it - the mirror should be cold. Also you could blow on the mirror - it will either come back at your face (the atoms in each version of you's breath will bounce off each other) or show up as condensate, depending on which world it is. I think (I'm not sure I understand it) but I think that light changes polarization upon reflection. So you could shine a laser through a polarizing filter at the mirror/plane, and then measure it again using a polarizing filter in the exact same orientation. If it were two worlds, the second filter shouldn't change the amount of light that comes through, while if it were a mirror, I think it might.

Edit for more info:

After looking around a little, it seems like measuring the polarization would work.

...In other cases, light is polarized because it has undergone a process that has preferentially removed light of a certain polarization. For example, when light reflects off of a surface, those light waves that have their electric field oriented in the plane of reflection (in the plane defined by the incident and reflected rays) is more likely to be refracted (light with this orientation of electric field is often referred to as p-polarized light). Light waves that have electric fields oriented perpendicular to the plane of reflection (s-polarized light) are more likely to be reflected.

http://www.photonics.com/Article.aspx?AID=35808

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