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After watching some ants in my garden today, and then looking at this very illuminating demonstration, I got to wondering, about what they would see. Not specifically ants (I understand their eyesight is quite poor), but similarly small, or even smaller creatures.

I guess I'm asking more about the nature of light and how photons are reflected off very small surfaces. Would a very small creature, like say, an ant, with vision, be able to see something as small as a single e. coli bacterium? or a virus? Would their world 'look' the same as ours or does the viewers relative size have a bearing on the quality of their perception?

And additionally beyond the realm of reality, if I could shrink myself down to the size of a bacterium, could I see atoms?

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One of the unfortunate laws of nature is that to see more detail you inevitably need bigger and more complex optics. – Martin Beckett Jul 23 '12 at 20:28
@MartinBeckett This is true of optics that see the farfield, but if you include the evanescent field, then the possibilities change altogether. See my answer. – WetSavannaAnimal aka Rod Vance Feb 18 '14 at 11:44
Sam, wonderfully imaginative question by the way. And I don't believe it's as simple as to see better you need bigger. – WetSavannaAnimal aka Rod Vance Feb 18 '14 at 11:45

4 Answers 4

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The other answers to the effect that one needs big optics to see fine detail are indeed true for are true for conventional imaging optics that sense the electromagnetic farfield or radiative field i.e. that whose Fourier component at frequency $\omega$ can be represented as a linear superposition of plane waves with real-valued wave-vectors $(k_x,\,k_y,\,k_z)$ with $k_x^2+k_y^2+k_z^2 = k^2 = \omega^2/c^2$. This is the kind of field which the Abbe diffraction limit applies to and limits "eyes" like our own comprising imaging optics and retinas, or even compound eyes like those of an ant.

However, this is not the whole electromagnetic field: very near to the objects that interact with it, the electromagnetic field includes nearfield or evanenescent field components. These are generalised plane waves for which:

  1. The component of the wavevector in some direction $k_\parallel$ is greater than the wavenumber $k$ and can thus encode spatial variations potentially much smaller than a wavelength;

  2. The component of the wavevector $k_\perp$ orthogonal to this direction must therefore be imaginary, so that $k_\parallel^2 + k_\perp^2 = k^2$ can be fulfilled.

So such fields decay exponentially with distance from the disturbance to the electromagnetic field that begat them and thus cannot normally contribute to an image formed by an imaging system.

However, if you can bring your image sensors near enough to the disturbance, you can still register the detail encoded in the finer-than-wavelength evanescent components. This is the principle of the Scanning Nearfield Optical Microscope.

The near field optical microscope sensor can be extremely small indeed, so that a bacterium sized lifeform could register below-wavelength detail in the World around it with receptors built of a few molecules as long as the lifeform were near enough to the detail in question. Note that, when $k_\parallel > k$ that the fields decay like $exp(-\sqrt{k_\parallel^2-k^2} z)$ with rising distance $z$ from their sources. So there is a tradeoff between how much finer than a wavelength we can see with such a sensor, and how near to the source we need to be to see it. If we want to see features one tenth of the wavelength of seeable light, then $k\approx 12{\rm \mu m^{-1}}$ and $k_\parallel \approx 120{\rm \mu m^{-1}}$, so that the amplitude of the nearfield decays by a factor of $e$ for each hundredth of a wavelength distant from the source the detector is. Thus we lose about 10dB signal to noise ratio for every hundredth of a wavelength distance that separates the detector and source. So to sense such fine detail (50nm structures) from a micron away would need extremely strong light sources, so that the detectors would have a very clean signal.

Of course, the above is an extreme example, but if you're a bacterium sized lifeform directly sensing the field using a finely spaced array of molecular sensors, you may well be able to "see" below-wavelength features of the World in your immediate neighbourhood. Moreover, it is possible to conceive of a tiny creature "feeling" its neighbourhood using molecular atomic force microscopes.

So, yes, if you include all physics and heed the proviso that you must get up really close to the sensed objects, it would be possible for a bacterium sized lifeform to see below-wavelength detail in its immediate neighbourhood, maybe even individual atoms if we include atomic force sensing.

Of course, packing all the signal processing "brain" into the lifeform needed to understand this information might be another matter altogether.

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Ants only have low-resolution eyes, aside from three ocelli - simple eyes - that only detect an overall light level and polarization, see

Their ability to see details - small objects and their features - is much worse than for vertebrates like us. To suggest that animals - especially as primitive animals as ants - could see bacteria is preposterous.

The wavelength of visible light is about half a micron - which is also the size of many bacteria. So you can't see anything inside bacteria with the visible light, not even with cutting-edge technology. To see more detailed objects, you have to switch to X-rays or electrons and create better microscopes.

It's even more unrealistic to propose that one - or even an ant - could see an atom (which is 10,000 times smaller than a bacterium) through visible light.

You can't just scale things up and down. The world is not invariant under scale transformations, we say. Different length scales see different kinds of physical phenomena and different physical objects. The atom of a given kind has always the same size and you can't scale it up. Moreover, you didn't even do the scaling properly because you didn't scale the wavelength of the light. Also, vision with detailed resolution requires some "large enough circuits" to deal with the information etc.

By the way, this holds even for accelerators. The LHC is our best "microscope" that can see distances shorter than $10^{-19}$ meters - but to do so, it requires tunnels with the best magnets that are 27 kilometers long. Objects as small as ants can't see with this good resolution, and even if they could, they couldn't deal with the huge amount of information that their eyes would be giving to them.

Large enough animals - e.g. mammals - see the world much like we do. There are well-known differences between the colors that different mammals are sensitive to. Dogs are, for instance, partly color-blind, relatively to what we can do.

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The asker specifically stated in the question that the vision of ants was just a metaphor, and his question was about the nature of light. It is not "ludicrous" to propose the question, as you felt the need to state more than once. It is ludicrous to berate newcomers to this forum for asking questions, as you did to me just a moment ago (link follows), and to this asker just now. – Olhovsky May 9 '11 at 7:16
Dear Olhovsky, you're not right - or what's the right way of saying that you're wrong without berating you. ;-) The idea that one can see bacteria or atoms is ludicrous mainly and exactly because it contradicts the basic nature of light, namely that it is made of waves. One may use any metaphors but at the very end, physics has a content that is not a metaphor. In my country which is not at the cutting edge, the fact that the light is made of waves is being taught at basic schools so I reserve the right to say that people unfamiliar with this very point lack some basic education. – Luboš Motl May 9 '11 at 9:35
And if the issue is about newcomers, let me say that I find the recent flood of low-quality questions frustrating, indeed. The purpose of this server is not to attract a maximum number of random "newcomers" who write arbitrary sequences of words with at least one question mark. Just a few months ago, this was supposed - and nearly was in practice - a genuine server to ask and answer questions about physics by people who actually know some physics. - And thanks, Robert, by the way. – Luboš Motl May 9 '11 at 9:36
@Luboš, I agree the quality of Questions has decreased, but I think people who actually know some Physics are not asking Questions, for whatever reasons. When newcomers arrive, they immediately find examples of Questions that seem to them more stupid than their Question, so why not ask it? The hard Questions are hard to find, and are quite likely not to be Answered. If there were a preponderance of hard Questions, the low-quality Questions might be put off. What newcomers don't see, so they're not put off by them, are the Answers that tell the low-quality Questions that they're stupid. – Peter Morgan May 9 '11 at 12:10
Wow, I haven't been called stupid in so many interesting ways in quite a while. I apologize if the question was esoteric enough for you, I'll try and do better next time, but it was about physics, it wasn't about programming, for instance, so I'm not sure what your gripe is. If you thought so little of the question, why not vote it down and not answer it? Also, I didn't "propose" that one could see atoms, I asked, and it theoretical, not practical, but assuming perfect resolution, then, and using visible light, what would the world "look" like at that scale? – Sam May 9 '11 at 14:55

The ant world is ordered far more by chemical reception and pheromones than by vision. Ants produce an array of such chemicals which act as signals. They also sense other chemicals in their environment, and as what might be called a “super organism” they have some collective map, a chemical map, of the terrain they inhabit.

Ants have compound eyes, and they are pretty small. For the most part their purpose is to sense sudden changes in light levels. An ant which perceives such then gets a signal that some predator might be present and so getting out of there is in order.

Some species of baceteria have opsin molecules that are photoactive. So the reception of photons can result in changes in molecular pathway activity. The rhodopsin molecule in our eyes or retina has two conformal states for reception and nonreception of a photon. The energy of the photon changes the shape of the molecule and this then acts to initiate a GTP molecular pathway which is amplified ultimately into a neural action potential. Rhodopsin is one form of opsin molecules, which in their general classification overlap with photosynthetic molecules in some bacteria as well. However, the bacilli do not form any sort of image of anything.

In order for a bacillus to “see” an atom they would need to detect gamma rays. Gamma rays are largely outside the EM spectrum available to biological systems. In fact they are lethal.

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I see you were demoted once again :) . – anna v May 10 '11 at 4:37
I've merged the two instances of your account(s). You can flag for moderator attention when that happens. – dmckee May 10 '11 at 14:12

As far as the function of light goes: Yes you can scale down (to a point). I have worked on an ASIC (Application Specific Integrated Circuit) which used an 8 micron process (Cro-magnon by today's standards). I could not see the detail of these circuits in the finished product (far too small) BUT they were made basically (I am greatly simplifying) with itsy-bitsy photographic images produced by light (beyond the range of visible light). To say it another way: the resolvable detail available from light is far, FAR finer than the un-aided human eye can see.

Biologists claim that eagles can see about 10x sharper detail than a human (and an eagle's eye is noticably smaller than a human eye).

What I don't know, is where the physical size of the eye limits detail. I see no reason why it couldn't scale down... WAY down. But I am not a biologist and (thankfully) not an ant. It would be interesting to find out where the smallest eyeballs end and where other seeing apparati take over.

So, your example of getting down to where you could see bacteria presents an interesting break point: There is theoretically no problem seeing a bacterium (size about 1000 nm) at the lower end of UV (upper end of human-visible) light, wavelength about 400 nm. But detail would obviously be a bit hazy. The bacterium would appear as a blurry blob, and no glasses would help. The theoretical limit for modern optical microscopes to resolve detail is 200 nm (using 550 nm "green" light).

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