Here’s a fun thing that has been zipping around the internets this week: a collection of “back of the envelope problems” put together by Edward Purcell. Hours of fun reading if you’re the kind of person who likes to spend their leisure time doing word problems (and I mean that in the best possible way).
One of Purcell’s problems is labeled “Electromagnetic energy in your eyeball,” and it concludes with a provocative (and true) observation. The problem asks the reader to calculate the total energy in all the photons that are inside your eyes at any one moment. Roughly speaking — which is the point, since we’re doing back-of-the-envelope problems — these photons come from one of two sources: the visible light from the outside world that enters your pupil, and the infrared light that is emitted as blackbody radiation from your eye itself, since you are an object at body temperature. Purcell suggests that you compare the amount of energy from each source.
And the answer is: there is much more electromagnetic energy in your eye at any one moment from the infrared radiation you’re emitting yourself, than the pittance of visible light you get from the outside world. Between 100,000 and a million times as much. Which raises a question we may never have thought to ask: why does it get dark when we close our eyes? The amount of electromagnetic radiation hitting our retinas hardly changes!
Purcell’s last sentence gives the answer: “Only quantum mechanics can explain why that makes it dark!”
We see light when photons of an appropriate wavelength reach the photoreceptor cells in the retinas of our eyes. The energy from the photon is converted into chemical energy via phototransduction, which sets an electrochemical signal to the visual cortex. (Presumably unnecessary disclaimer: everything I know about vision I learned from Wikipedia.) In particular, the photons are absorbed by a chemical called retinal, which isomerizes from the 11-cis state to the all-trans state. (That last bit was a blatant cut and paste.)
Here’s the part I do understand: isomerization is a matter of nudging a chemical from one structural form to another, without actually changing the chemical formula. Molecules have energy levels, just like electrons in atoms, and in order to effect the change in the retinal via photoexcitation, a photon has to have enough energy to cause a transition between the isomers. That’s a matter of quantum mechanics, full stop. Molecules can’t take on just any old energy; the allowed energies are quantized. As a result, it doesn’t matter that the infrared light inside your eyeball has much more energy than the visible light from the outside world; the energy comes in the form of individual photons, none of which has enough energy to get the reaction going. It’s very analogous to the photoelectric effect in metals, for which Einstein won his Nobel prize.
We often say that quantum mechanics applies to the world of the very small, and involves mind-bending alterations of our everyday reality. Which is true as far as it goes, but the more simple truth is that quantum mechanics applies to absolutely everything. It underlies how the everyday world works, from the stability of matter to the darkness when you close your eyes.
What an interesting topic. With my eyes tightly covered ( or open in total darkness ) I see countless infinitesimal points of light on a black background. The points are of every color. It is impossible to focus on any single point as all are in slow “Brownian motion.” The same vision is present in daylight with eyes open, but it is overwhelmed and unnoticeable.
Like others, I can see geometric figures or faces if I wish to, but, as in my technicolor nocturnal dreams, I lack conscious control over them. Some tell me that they see only blackness without feature, or that they dream in B&W, but I suppose them to be observers less critical than physicists who all see precisely what I see.
That’s a really nice example of quantum effects.
Snakes have heat-sensing organs (even blind ones are able to detect prey)
These are small pits located above the mouth.
They have an Infra-red sensing mechanism.
Unlike the eye, it doesn’t use phototransduction, but a temperature sensing ion channel.
The blood supply to this organ keeps it cool, maintaining its sensitivity to the environment.
@ryan (#1) Two-photon infrared photon absorption does indeed occur in the dark but at a much lower rate and isotropically, so it will appear as noise on your retina, as opposed to the green point of a directed infrared laser (#25 by @sledgehammer).
So what about the UV limit? There’s a bit of low frequency UV that’s not massively absorbed by water.
I was going to write the same thing as post 14. The correct physics is likely semiclassical in nature, just like most of chemistry is. It involves parts that can be only explained by quantum mechanics (like carbon resonances) and parts that are decidedly classical.
Further, there is a major problem with the quantum mechanics only explanation. Consider a source of light that increases in intensity vs one that changes in frequency.
Immediate problem.. Why does the absorption by your eyes act like it was classical when your eyelids are open (eg it responds to changes in intensity, but not frequency) but not when they are closed.
Further, it strikes me that the chemistry changes in an abrupt manner when your eyelids close (for one there is a film of fluid that makes contact with your eyes, as well as extra pressure)
It would be interesting to know how this result changes when you include focusing of eye lens into account.
Actually, the visual pigment can absorb well into the IR. Very weakly, but it does absorb. The absorption spectrum is quite broad and there is not at all a discrete cut-off in terms of a photon not providing enough energy. If quantum mechanics can apparently explain the absorption spectrum of the visual pigment that would be fantastic, as we only have empirical models at the moment (i.e. nobody knows how to derive the absorption spectrum from the chemical structure of opsin).
In addition to the weak absorption in the IR, the pigment is situated all along these narrow little optical fibers called photoreceptors. Light radiated “cross-ways” into these will not undergo total internal reflection, not be coupled into the “fiber” and so will tend not to interact with much photopigment. Conversely light coming through the pupil is maximally coupled into these and so interacts with the most photopigment. This effect is so pronounced that light coming through the center of the pupil is quite noticably brighter than light coming through the edge (see: the Stiles-Crawford effect).
Very interesting. But shouldn’t the answer be a simple “because human eyes do not see the infrared spectrum”? Same with UV. If we saw infrared, then it seems everything would be bright when our eyes are closed (makes sense just from the fact that our eyeballs are close to 100F body temp).
Sean,
since you’re becoming a science rock star, here is an interesting QM experiment for you to look at
http://deanradin.blogspot.com.au/2012/05/consciousness-and-double-slit.html
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i have a question….i am not a physicist…but isn’t this the same reason why we cannot see infrared even when our eyes are open?….i mean i did not understand why this was portrayed as a puzzle, as from primary school we were taught, we can only see VIBGYOR…or am i missing something here..please let me know
@2 (byby): matter of opinion. I used Purcell for first-year undergrad, and hated it – the upper division course used Griffiths, so I looked at that, and it made so much more sense to me. Maybe I’d like Purcell now, but I’ve seen too many times when a teacher thinks a book is awesome, and the students detest it, because their perspectives are so different.
#37 (himadri): sure, it’s the same reason why you can’t see IR when your eyes are open. But the point was in terms of numbers of photons, it really doesn’t matter whether your eyes are open or closed (the visible photons are a rounding error). Given that, why does it make a difference when you close your eyes? QM explains why your eyes respond only to visible light, and don’t react to the much more abundant IR.
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hello charon…thank you for your reply….i have a question..a pit viper who can see in IR, what does it see with eyes closed and open?….when it has eyes closed, so only IR from eyes is inside, what does it see in that IR?..and when its eyes are open, what does it see then when there is IR from body heat, IR from surroundings all there?
Himadri, read my reply above. The vast majority of these internal-eye IR photons are not going to get coupled into the photoreceptors.
Also, there is IR, and then there is IR… I’m not sure where the peak of “pit viper” IR sensitivity is compared to the wavelengths of IR that we are talking about here.
Actually a directly visible effect of the quantized form of light occurs at very low light level. If in an almost, but not totally, dark room one watches a just perceptible uniform surface, what is seen is not a uniform surface, but a constantly fluctuating surface. A back-of-envelope calculation shows that these fluctuations are consistent with the expected photon noise. Thus the eyes might directly perceive that light is made of quanta, a feature that Newton could have inferred. (This is analogous to showing the molecular nature of matter from the Brownian motion of dust particles.) Of course this perception of fluctuations is not a solid proof before determining if the vision system is not itself producing most of the fluctuations.
Oh well, this blog post answered a lot of questions I had previously.
Quantum mechanics isn’t really an answer though. Not to me, anyway.
Thanks! This was award winning stuff. Sorry, Sean.
Tsk-tsk on the copy-and-paste method of education. 😀
The solution is not complete – when you close your eyes, there is still intrinsic noise “dark noise”, due to spontaneous thermal conformational changes of retinal, which give rise to the photocascade and sets about flow of ions through the membrane of the photoreceptor outer segment disks. This creates a current of the order of 1 picoAmp, which is indistinguishable from the current due to a single photoisomerization of retinal molecule; hence we don’t really see complete darkness in a dark room (or complete absence of sound in a sound proof room). This has to do with the stability of the molecules…
@Alex #18 The smoothness of a high-pass filter’s roll-off is due to properties of the components which are not mathematical ideals. Likewise, high-pass filters in quantum mechanics are only exact insofar as you ignore idealizations. For instance, a quantum mode in a cavity can only be excited by an *exact* energy eigenstate when the cavity is assumed to be ideal. But this isn’t true in real-life; all cavities and other methods of quantum excitation have finite bandwidth which never go precisely to zero. Quantum mechanics and classical mechanics are not distinguished by the presence of mathematically exact zeros.
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Everyone seems to be ignoring the fact that 200 billion neurons w/trillions of interconnections in the occipital lobe alone are processing what we “see” due to millions of years of evolution. The physics of retinal chemistry is important, but to concentrate on just that ignores an incredibly complex multivariate interaction with which we have only scratched the proverbial surface.