Quantum Mechanics When You Close Your Eyes

By Sean Carroll | May 25, 2012 11:22 am

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.

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  • ryan

    two-photon microscopy works by having two low energy photons absorbed simultaneously (they add up to one quantum of energy presumably). Why does this not occur? My best guess is it does but it’s too rare to be perceived.

  • byby

    Best EM book ever written is by Purcell and they is it at Caltech for frosh classes!

  • Chris

    Superman must have a nonlinear crystal in his eyes to upconvert the infrared into visible laser beams. :-P

  • MPS17

    Well, if you’re going to go there, it’s only because of QM that you know how to calculate the energy in thermal radiation to begin with.

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  • http://thefloatinglantern.wordpress.com Tim Martin

    So the photons emitted from the eye (infrared) have more total energy than the photons entering the eye from the outside world (visible light), however each individual infrared photon has too little energy to cause isomerization? Is that correct?

  • giganotosaurus

    Bill Bialek (Princeton Physics), who has been researching and teaching biological physics for many years, has a nice description of rhodopsin and vision. A link that hopefully still works is:

    http://fora.tv/2010/11/03/More_Perfect_Than_We_Imagined_A_Physicists_View

    Bialek has been one of most influential people discussing physics principles (e.g. stochastic physics and quantum mechanics) in living systems. If you liked Berg and Purcell, or P. Nelson, you’ll most likely enjoy his work too.

  • http://Facebook Bashir Bomai

    Yes Tim.You are correct but I haste to posit that these energies maintain a kind of balance which is not fully understand.The answers are there.Even as you read my feedback,the energies are at work.The individual IR photon maintains its energy and the isomerization does take place.If you find yourself in the dark,the moment you begin to adjust,something kicks in and you make out objects.However,one needs large doses of intuition in order to percieve certain things in QM.I beleive it is so.

  • Samuel A. Falvo II

    @Tim — yup, that’s exactly it!

  • Joe

    Neat. Does it follow that in general, animals with body temperatures on the order of 300 K can’t see in the infrared? If we had some other molecule in our eyes instead of retinal, and that molecule could be isomerized by IR photons, presumably the signal-to-background ratio would always be too low for us to see anything…

  • Samuel A. Falvo II

    @Bashir – you observe things at night because our eye secretes a chemical which makes our rods (note: not cones!) more sensitive to lower light levels (something called xxx purple, forgot what the ‘xxx’ is). The disadvantage is you only see in black-and-white. The cones are less sensitive to light, but give us the ability to sense color.

    EDIT: xxx purpose == visual purple, also known as rhodospin. Thank you Wikipedia.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    Was the allusion to Einstein’s “Is the Moon only there when you look at it” intentional?

  • Chris

    An interesting similar back of the envelope calculation of why cell phones don’t cause cancer is given at http://bobpark.physics.umd.edu/WN12/wn050612.html :
    “Cancer is linked to the formation of mutant strands of DNA. More than 100 years ago in his 1905 paper on the photoelectric effect, Albert Einstein predicted an abrupt threshold for photoemission at about 5 eV, just above the lovely blue limit of the visible spectrum, demonstrating wave-particle duality. He was awarded the 1923 Physics Nobel Prize. Its also the threshold for the emission of invisible ultraviolet radiation that causes hideous skin cancers. The cancer threshold, is therefore, 1 million times higher than the microwaves band. The same enormous mistake was made in the 1980s when epidemiologists falsely warned that exposure to power line emission can cause cancer. Power lines abruptly stopped causing cancer in 1997 after the U.S. National Cancer Institute conducted a better study. “

  • Igor Khavkine

    Consider a hypothetical eye that works using only a classical mechanism. Say, the light receptor molecules are replaced by classical charged oscillators with a very sharp frequency, which lies far away from the peak energy density of the thermal radiation within the eye. Modeling these classical light receptors as damped harmonic oscillators driven by the EM field within the eye shows that the energy transfer is maximal at the resonant frequency and strongly suppressed away from it (a higher “quality factor” means more suppression). Such an eye would also see darkness when the eye lids are closed.

    Quantum mechanics is certainly involved in how our actual eyes work, but perhaps singling out this feature and implying that it would be impossible without quantum mechanics is a bit of a reach. Of course, I’m taking issue only with this particular narrow interpretation of Purcell’s statement.

  • http://www.uweb.ucsb.edu/~criedel/ Jess Riedel

    These kind of quantum mechanics sound bites make me a bit queasy, mostly because they are handy-wavy about which parts are classical, and which are quantum. I don’t think the claim is that quantum mechanics is necessary for phenomena that have a frequency cut-off; there are plenty of low-pass and high-pass filters in macroscopic, classical electronics. So the claim must be that *this* particular system relies on quantum mechanics to achieve its high-pass filter. But I think in order to say something like that, you have to be precise about what a classical version of this particular system would look like. I don’t think it’s enlightening to just assert that the classical version would be sensitive to total energy, regardless of frequency, and then say quantum mechanics must therefore be responsible.

    For instance, it might be true that the stability of matter is due to quantum mechanics, in some sense. Certainly, classical E&M point charges wouldn’t form stable matter. But it’s also obvious that one could invent a sufficiently complicated classical model which looks liked stable matter on large scales. So the mere observation of stable matter is not enough to prove that quantum mechanics is somehow especially important for stability.

  • David Pollard
  • http://wealthofnotions.blogspot.com/ Adam_Smith

    I agree with Igor Khavkine who shows how classical electromagnetic wave theory might have explained the insensitivity on the eye to infrared radiation. It should additionally be noted that there were classical corpuscular theories of light, the most notable being that of Sir Isaac Newton. Such theories were also “quantum” in their way and could be applied along the same lines as modern quantum theory to explain this particular problem.

  • http://alexpavellas.wordpress.com Alex

    @jess #15: if the eye were modeled as a classical high pass filter, there would still be a response to infrared wavelengths, even if there was a very steep roll-off. In the quantum version, there is zero response to IR radiation, which is what makes it different. For the classical version, a high enough intensity of IR radiation could be seen.

  • Brett

    Is it just me? when I close my eyes, I swear I still see variations in the “darkness/shade of black”. I think it’s similar to your ears. If you can enter a sound proof room and insulate it very well, blocking out all sound from the interior and exterior, then you’ll hear a ringing in your ears. The ringing is the sound of your nervous system. I’m guessing both are the same thing, a kind of feedback to from hooking sensors up to a source of power…or it’s the LSD.

  • Toiski

    Brett: Yes, I see it as well. I don’t think it’s background activity in the visua cortex, because pressing slightly on your eyelids modulates the phenomenon. It seems to be something happening in the eyes themselves. It could either be pressure triggering the photosensitive cells or the connecting neurons, or the pressure could increase the temperature of the eye matter slightly and cause more of the “double-absorption” events mentioned by ryan (1.). I think the pressure triggering explanation is more likely.

  • http://twitter.com/#!/JEB54 John Branch

    Isn’t this just a QM explanation for why our eyes don’t happen to see in the infrared? That means what we’re talking about here is not only why it’s dark when we close our eyes but also why we see nothing with our eyes open if there’s no visible light around.

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  • http://www.sevenchakrasmeditation.com Seven Chakras Meditation

    This was a great article. I have learned a great deal about quantum mechanics. I have a question. When I close my eyes during meditation, I see many different rays of light that keep changing, sometimes, I can see people’s faces from centuries ago because of how they are dressed. What cause that?

  • http://ziblink.deviantart.com/ Ziblink

    Brett: I know if I go outside on a sunny day and shut my eyes I can see the inside of my eyelids. Oddly, if I wave my hand in front of my face while doing this I see strange geometric patterns.

  • sledgehammer

    I work around high power infrared lasers, and we have a saying: without your protective goggles, the last thing you’ll see is a very bright flash of green.
    At high enough power, everything (except a vacuum) becomes optically non-linear, and the 1.06 um wavelength of the YAG laser will be doubled to 503 nm (green) in the vitreous humour of the eye via 2-photon absorption.

  • Marcos

    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.

  • Terry Bollinger

    That’s a really nice example of quantum effects.

  • prianikoff

    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.

  • http://commonsensequantum.blogspot.com Arjen

    @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).

  • tcmJOE

    So what about the UV limit? There’s a bit of low frequency UV that’s not massively absorbed by water.

  • Haelfix

    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)

  • tadas

    It would be interesting to know how this result changes when you include focusing of eye lens into account.

  • Melf_Himself

    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).

  • brucem

    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).

  • MKS

    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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  • himadri

    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

  • Charon

    @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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  • himadri

    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?

  • Melf_Himself

    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.

  • Daniel Pfenniger

    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.

  • Gizelle Janine

    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. :D

  • Vengu

    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…

  • http://www.uweb.ucsb.edu/~criedel/ Jess Riedel

    @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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  • Mark Denison

    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.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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