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.
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.
Best EM book ever written is by Purcell and they is it at Caltech for frosh classes!
Superman must have a nonlinear crystal in his eyes to upconvert the infrared into visible laser beams. 😛
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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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?
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.
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.
@Tim — yup, that’s exactly it!
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…
@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.
Was the allusion to Einstein’s “Is the Moon only there when you look at it” intentional?
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. “
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.
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.
Is it not simply that there is a notch in the absorption spectrum of water which corresponds to the visible spectrum?
See, e.g.,
http://www.google.co.uk/imgres?imgurl=http://people.seas.harvard.edu/~jones/es151/gallery/images/segelstein81.gif&imgrefurl=http://people.seas.harvard.edu/~jones/es151/gallery/images/absorp_water.html&h=384&w=565&sz=8&tbnid=Hggq6XjlHQNQBM:&tbnh=91&tbnw=134&prev=/search%3Fq%3Dwater%2Boptical-absorption-spectrum%2Bwavelength%26tbm%3Disch%26tbo%3Du&zoom=1&q=water+optical-absorption-spectrum+wavelength&usg=__SrxSyi7b0-o976QwjfJSKBzNduU%3D&hl=en&sa=X&ei=SBHAT7qiEIaq8AP6wrHBCg&ved=0CCkQ9QEwBw&gbv=1&sei=WxHAT5G_OIrY8APZupXDCg
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.
@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.
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.
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.
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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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?
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.
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.