# Magic Mirror on the Wall, How Do You Even Work at All?

**Bernard Murphy, PhD, Chief Technology Officer, Atrenta Inc.**

12/1/2014 05:45 PM EST

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The more one looks into it, the more one realizes that aspects of mirrors that initially appear to be intuitive are, in fact, extremely hard to explain.

I'll call the other track "mostly classical." As far as I can tell, it is represented solely by Feynman and a Geneva University theoretician who applied the Feynman path approach to detailed calculations of reflection, refraction, diffraction, and other phenomena in 2005. This paper is quite technical but still worth a read. Though all other authors acknowledge Feynman's genius, it seems that few if any actually use his methods in QED calculations, because they are typically more complex to apply than Schrodinger-based approaches.

The Geneva paper seems to be the first time anyone has documented detailed consequences of the Feynman model. (Feynman didn't record his own calculations for this example.) But before I go there, let's look quickly at the other problem: that phase assumption. Path length is certainly a factor in phase at detection, but what about the phase when a photon starts on one of these paths? If the source is a laser, you can assume phases are equal at creation, but this is not the case for a regular light source. If you assume that amplitude summing (interference) at the detector is between different photons travelling on different paths, path differences still affect the result, but lack of correlation between source phases will lead to random and time-varying (noisy) interference at the detector, which is not what we see.

Back to what the Geneva paper has to say:

- Feynman's explanation is more fundamental and more powerful than the Schrodinger approach. Schrodinger can be derived from Feynman, but not
*vice versa*, because Feynman represents correlation between space-time events (between paths), but Schrodinger cannot. - In detailed calculations using the Feynman method applied to photons, all classical behaviors of light as waves emerge as expected. Reflection, in particular, follows Feynman's example.
- Photons propagate over macroscopic distances in a completely classical manner. (Heisenberg applies to the creation and detection of a photon and to scattering events, but not to simple propagation.) But we must consider all possible paths in the analysis.
- Paths add in the same way that waves add. We add amplitudes with phases to obtain interference at the point of detection.
- This brings us to the creation phase issue and the only conceptually difficult requirement of the Feynman method. Different photons have random relative phases at creation, but any given photon is trivially in phase with itself when created. Therefore, to obtain the results we see, interference cannot be between different photons travelling different paths. Each photon individually must travel along all possible paths and (indelicately) interfere only with itself at detection. This is the only way we can avoid that noisy interference between uncorrelated photons, and it is why experiments testing one photon at a time give the same results as for multiple photons at the same time.

I should caution that the 2005 paper is an interpretation, and that it makes predictions of new behaviors that have not yet been tested. But absent counterexamples, I find this interpretation very appealing. It is in complete agreement with Feynman's explanation, and it conserves all classical and intuitive understanding of light behavior based on photons, with just one exception. That exception is a doozy: A photon must travel simultaneously along all possible paths to the point it is detected and resolve itself through self-interference at detection. If we suspend disbelief on this one point, everything else is completely intuitive.

So what do we make of this one difficult point? Travelling simultaneously along all possible paths is definitely neither classical nor intuitive. Perhaps we see a particle travelling along all paths as a projection from a simpler path in something more fundamental than space-time. There are hints of this in a recent article, "A jewel at the heart of quantum physics," which suggests that the space-time so familiar to us may not be the most basic representation of reality. Whether we will appreciate this as an improvement in intuitive understanding is up for debate.

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McChalium_II 7/7/2015 2:56:13 PM

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Terry.Bollinger 12/3/2014 11:10:02 PM

To achieve this transformation physically, you would have to take a very thin rubber mold of, for example, your own face. The mask would need to transfer colors and textures to both sides. Once made, you would next need to flip the mold inside out and force yourself to imagine the now-convex inside surface of the mask as the outer surface of a real face. Our brains don't readily accept that severe of a transformation to a solid face, unless maybe you are Hannibal Lecter, so they instead try more "reasonable" transformations such as left-to-right or up-to-down. The visual outcome is similar, at least if you don't worry about the lack of solidity behind the image.

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GSKrasle 12/3/2014 8:13:58 PM

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mike_coln 12/3/2014 6:14:16 PM

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Terry.Bollinger 12/3/2014 1:41:00 PM

Using box-shaped room coordinates, stand near the back wall of a room that has some kind of text, say a poster, on the far wall in front of you.

Hold a flat mirror out to your left, keeping it parallel to the left wall of the room, and look at the poster image in the mirror. As you would expect, you will see the poster inverted left-to-right, and unchanged top-to-down. No big surprise there, right?

Now circle your arm upward in an arc until the flat mirror is instead parallel to the ceiling. Look at the image of the poster again. What do you see?

The same poster... only this time it is inverted

up-to-down, andunchangedfrom left-to-right...Uh, say what?

What's even more fun is that if you move your arm smoothly and keep the poster image centered within the mirror frame at all times, you can watch every step in the

continuoustransition between the "standard" left-to-right inversion and the unanticipated up-to-down inversion. Be sure to ask yourself when, exactly, the transformation takes place... }8^)>(Meanwhile, if you like quantum stuff, don't forget my earlier reply below about how

allforms of reflection and refraction require quantum mechanical "scoping out" of the human-scale shapes of large objects. The quantum world is always watching you, quite literally!)Author

GSKrasle 12/3/2014 12:24:25 PM

EXACTLY.

As I touched on a couple of months ago (http://www.eetimes.com/messages.asp?piddl_msgthreadid=46313&piddl_msgid=322067#msg_322067):

because of our psychology and bilateral (near-) symmetry, we have a hard time understanding until we abstract the question into symbolic form.

While not strictly "mirror"-related, the geometry of (chemistry) chirality is as hard to believe: if any two bonds of a chiral atom are exchanged, the result is the mirror-image of the original; exchanging another random two returns it to the original state.

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traneus 12/3/2014 10:58:57 AM

"Why does a mirror swap left and right but not up and down?"

A mirror swaps front and back.

The front (closest to the mirror) part of the object is the front (closest to the mirror) part of the reflected image. The back (farthest from the mirror) part of the object is the back (farthest from the mirror) part of the reflected image.

The left and right swap is our interpretation of the front and back swap. Due to gravity, we find rotating about our head to foot axis much more plausible than rotating about our left to right axis.

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Max The Magnificent 12/3/2014 10:03:00 AM

anyone interested can look up this short essay onYour Quantum Mechanical Eye.Hi Terry -- thanks for this -- I just took a quick look -- I'll be returning to peruse and ponder your essay in more depth as soon as I get a free momen

t.Author

Terry.Bollinger 12/2/2014 7:41:28 PM

In terms of

QED, however, thatiswhat happens. Feynman just doesn't get into that level of detail in that short, intentionally non-mathematical book.That is, all of those "not really there" photons in the path integral really

doend up bouncing randomly from all of those thermal atoms. However, since the total amplitude added by each such impact is proportional to the amount of turf occupied by the atom, the individual reflections are very weak. And while you might expect so many reflections to add up to a powerful overall effect, the fact that they are both random and complex (vs real) values means they tend very strongly to cancel each other. Only those components of the reflections that are in phase, e.g. due to long-range order (smoothness) in the mirror, will ever add up into a "signal" (amplitude, square root of the probability) that makes it likely the photon will travel in that direction. A fairly accurate classical analogy would be an ocean wave reflecting from a rough stone wall, with the wavelets bouncing from individual grains of the wall corresponding to the atomic-scale, non-reinforcing reflections of the mirror.The answer I like best, however, is that

neither reflection nor refraction are really classical phenomena. That is,allforms of smooth, optically coherent light bending are profoundly quantum mechanical in nature, even when their outcomes can be expressed in simple equations. That's way too much to get into here, but anyone interested can look up this short essay onYour Quantum Mechanical Eye.Author

GSKrasle 12/2/2014 6:52:07 PM