How can we possibly see atoms?

John Sidles is a medical researcher and a quantum systems engineer. His major focus is on quantum spin microscopy for regenerative medicine. He is both Professor of Orthopedics and Sports Medicine in the University of Washington School of Medicine, and co-director of the UW Quantum Systems Engineering Lab. Watching various injury troubles at the Sochi Winter Olympics makes us wonder whether quantum sports medicine is an idea whose time has come. Well beyond some media’s overheated references to our athletes as “warriors” is a nice reality: John’s main project is for healing those injured in the armed services.

Today Ken and I wish to talk about John and his work in general. We especially like his title of quantum systems engineer.

John works on the interplay between two important disciplines: medicine and quantum mechanics. One might be surprised that what we conceive as research in quantum mechanics is so closely related to medicine, but it is. John received the prestigious 2011 Günther Laukien Prize jointly with IBM researchers John Mamin and Dan Rugar. This was for their work on quantum spin microscopy, specifically, that variety of quantum spin microscopy called magnetic resonance force microscopy (MRFM).

John is obviously very busy, yet he finds time to post thoughtful and well-humored comments on GLL and elsewhere. His comments are always interesting, often more than anything that Ken and I have to say. We thank John for all his many contributions.

## Catching the Waves

John works in a different world than we do, yet we feel that we have much in common. One difference, however, is that he is sometimes an author on a paper with a bit more co-authors that we routinely have: For example, this is the list of authors from a paper on gravity waves which appeared in Physical Review D:

Of course a Polymath paper can have even more co-authors, so perhaps we are not from such different worlds. In a sense this research is already Polymathic: it’s part of a huge scientific collaboration to use a big machine named LIGO, which stands for Laser Interferometer Gravitational Wave Observatory.

There are actually two main observatories, in Livingston, Louisiana and Hanford near Richland, Washington. These are far enough apart to detect differences in arrival time of searched-for waves for purpose of confirmation. Amazingly the local observation of a wave would consist of a displacement of only ${10^{-18}}$ of a meter, a billionth of a nanometer, nano-nano. Based on mainstream cosmological models of the strength of gravity waves from stellar collision events, the current apparatus still projected to have only a ${1/6}$ chance of an unambiguous observation within a 6-year timespan. Here is a picture of LIGO’s Hanford site, near where part of the Manhattan Project took place in 1943:

With only ${10^{-18}}$ tolerance, we’d fear it all being thrown off by a passing flock of birds. Well John has that eventuality covered—his wife Connie, a noted Washington birder, could be posted as a lookout.

The LIGO paper reported nothing. That is it reported something, and that something was nothing. In physics, non-detection acts like a barrier or lower-bound theorem in computational theory. Technically the paper gave an upper bound—on the possible strength of gravity waves emanating from relatively-nearby X-ray binary stellar systems. What’s neat is that gaining the 90% confidence in their result required not better observations of the very large, but rather control of the very small. Moreover LIGO itself is being updated with more-sensitive detectors, which should give better determination between models and measurements of the large. The fact that one can probe differences at all on finer than a ${10^{-18}m}$ scale is amazing, and it matters to all of John’s work.

## A Math Puzzle?

John works on “seeing” individual atoms. The ability to do this will have many revolutionary applications, including changing the way that medicine is performed. Given John’s interest in regenerative medicine—the repair of damaged tissues and organs—the ability to see an individual atom, to see proteins in action, will have a potential game-changing effect.

Okay seeing atoms is cool. But how is it possible? Here is a picture of a hydrogren atom:

 2013 article source

A question that Ken Steiglitz of Princeton raised a number of times to me, while I was on the faculty there, is this: Suppose you can only make objects with accuracy ${\delta}$. How can these be put together to make an object to tolerance ${\epsilon \ll \delta}$? This is the “dual” of seeing. Steiglitz’s dual question for detection would therefore be:

Suppose you can only make objects with accuracy ${\delta}$. How can these be put together to detect an object of size ${\epsilon \ll \delta}$?

Indeed. How is this possible?

A plausible conjecture is this: It is impossible to make objects with accuracy ${\epsilon}$, given only tools that have accuracy ${\delta}$ where ${\epsilon \ll \delta}$. The trouble is that this seems to be false. Everyday we—okay Intel and other companies—make chips that have object resolution below the ${30}$-nanometer range. Is this a counterexample? Or is it?

Let’s look first at what John and his team have been able to do. Then let’s return to the math problem raised here and see if the conjecture is actually true, false, or unresolved.

## MRFM

One of John’s papers on this work is here. It clearly is a computer theory paper since he uses Alice and Bob to explain what he is doing.

Magnetic resonance force microscopy (MRFM) is an imaging technique that I can define more easily by what it can do, than how it works. It can potentially see protein structures at scales beyond the depth of X-ray crystallography and protein nuclear magnetic resonance spectroscopy. It can detect image features that are not just beyond those of sports teams’ magnetic resonance imaging (MRI) machines, but are over a billion times more detailed than those currently used in hospitals.

Recall atoms are small, but “small” means they are about ${10^{-10}}$ meters in size, on the order of ${10}$ nanometers. They are much too small to be seen with light-based microscopes. They can be “seen” by a MRFM. These combine various techniques. They use an MRI, which is based on quantum spin effects, and combine that with a probe that was used for an atomic force microscope.

## Spacing Out Inner Space

Here is an example of how one can multiply the resolution of an object. The method is used in the lithography of integrated chips, to effectively double the resolution. We quote our friends at Wikipedia who use the following figure to explain this method:

A spacer is a film layer formed on the sidewall of a pre-patterned feature. A spacer is formed by deposition or reaction of the film on the previous pattern, followed by etching to remove all the film material on the horizontal surfaces, leaving only the material on the sidewalls. By removing the original patterned feature, only the spacer is left. However, since there are two spacers for every line, the line density has now doubled. The spacer technique is applicable for defining narrow gates at half the original lithographic pitch, for example. The spacer approach is unique in that with one lithographic exposure, the pitch can be halved indefinitely with a succession of spacer formation and pattern transfer processes. This conveniently avoids the serious issue of overlay between successive exposures.

Now let us return to our math puzzle. Here is an example from the Microscopy UK website. The grit is very fine so the ${\epsilon}$ is very small. Of course there still is the macro issue of the grinding motion and the amount of time spent doing that. But this seems to be okay with the conjecture: cannot one make ${\epsilon}$ smaller than the ${\delta}$?

## Open Problems

How low will we be able to go? Will computers take us beyond the standard tradeoff between scale and energy?

1. February 13, 2014 11:22 pm

Alexander Grothendieck where are you? You have a friend in Sidles.

February 21, 2014 3:00 pm

If I were to find a French equivalent to this great contributor to GLL, I’d rather choose Jean Dieudonné. Like him, he was a great scientific writer who had encyclopedic mathematical knowledge. By the way, he also wrote most of Alexander Grothendieck’s published work.

2. February 13, 2014 11:56 pm

As for the conjecture: Given that in pre-industrial times we couldn’t do much better than millimeter precision and now we can manipulate single atoms, somehow we must have increased our accuracy along the way.

• February 15, 2014 5:01 pm

I completely agree with Aram!

• February 15, 2014 5:19 pm

Gil, by the way your recent post including the Sidleses helped with the (r)esearch for this one, so thanks!

February 14, 2014 12:57 am

Oddly enough, LIGO’s Daniel Sigg and I do have a joing article on gravity wave detection: “Optical torques in suspended Fabry-Perot interferometers” (Phys. Lett. A, 2006). These results were derived within four different quantum frameworks:

Approach 1  quantum path integrals (never published), then

Approach 2  quantum field theory (in PLA 2006), as affirmed by

Approach 3  geometric ray-tracing (also in PLA 2006), as extended to

Approach 4  varietal flows (per the SHS Seminar “Green Sheets” for 2013; manuscript in preparation).

This exercise helped us toward a more nearly unitary appreciation of various, seemingly entirely disparate, approaches to understanding quantum dynamical flows. In particular, the varietal approach #4, which was born of a union of approaches #1-#3, has subsequently evolved to be a mathematically natural (we think) extension of them. As Feynman put it:

It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship. […] I don’t know why this is — it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. […] I don’t know what it means, that nature chooses these curious forms, but maybe that is a way of defining simplicity. Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.

To us quantum systems engineers, it seems entirely plausible that there remains plenty more to be discovered about quantum dynamical flows and how to simulate them efficiently … in service of purposes both fundamental and eminently practical. Which is good!

February 14, 2014 1:26 am

Suppose you can only make objects with accuracy $\delta$. How can these be put together to detect an object of size $\delta$?

Nature’s solution to this riddle has been presented in (literally) tens of thousands of academic lectures: whenever an irritating kilohertz-frequency feedback squeal, having sound-wavelength much less than one meter, is generated by a loudspeaker-microphone pair that are separated by a distance much greater than one meter.

This familiar-to-all phenomenon — in effect, spatial resolution-amplification mediated by resonant dynamics — was exploited in magnetic resonance imaging by Paul Lauterbur and Peter Mansfield (who received the Nobel Prize) and Raymond Damadian (who didn’t).

The really remarkable aspect of this STEM story (as it seems to me) is the long list of scientific and mathematical luminaries, including but not limited to Linus Pauling, Irving Langmuir, Norbert Wiener, Simon Ramo, John von Neumann, and Richard Feyman, who all thought hard about the problem of improving microscope resolution … and yet throughout four successive decades (at least) the world’s most elite researchers entirely overlooked the simple-in-retrospect resonant imaging insight of Lauterbur/Mansfield/Damadian.

Are comparably obvious insights being overlooked at present? In math, science, engineering, and medicine too? History suggests that the safe bet is “yes” … and this likelihood is good news for young researchers.

5. February 17, 2014 1:42 am

“Suppose you can only make objects with accuracy δ?” I think that there might be a lot of ambiguity in the notion “accuracy δ” which may allow different answers.

Also, Pip, can you explain why the Intel 30 nanometer capability is a counterexample?

6. February 17, 2014 2:20 am

Let me use this opportunity to join Dick and Ken in thanking John Sidles for his vision and contributions to science and engineering, for sharing over many scientific blogs his imense knowledge, ideas and insights, for his kindness to me and to everybody and his amazingly good intentions.

February 17, 2014 12:56 pm

Hey guys,

I have found the proof of the existence of one-way functions:

Good Luck!!!

8. February 18, 2014 5:43 am

It’s good to read John featured in an article!

As far as the question, the two most obvious answer are scattering as used in atomic colliders or non-linear heterodyning, (which is exploited in interferometry as I am sure John is familiar with) which can produce higher frequency sidebands.

I have played this mind game with trying to think about how one would detect Hawking radiation from a black hole. The problem being the background cosmic temperature is greater than the temperature of hawking radiation making it almost impossible to detect. One concept I started to work on was the use of a satellite that had detectors that looked like large dinner plates. Each detector plate would be able to measure temperature on either side. These plates would move forward an backward on some track in order to have a velocity that would cause red or blue shifts in the frequencies detected. One would have several pairs of these detectors at right angles. At least two of the detectors would face radially toward the blackhole. The system would be synchronized so that as one plate was moving toward the blackhole, the other would be moving away. The other plates at right angles would be performing a similar operation but on a tangent line to the orbit around the blackhole.

In principle, the tangent plates should have nearly identical temperatures detected, while the plates pointed radially should see slightly different temperatures. The relative motion of the plates would create an amplification of hawking radiation. The idea is to try to assess differential changes of the different frequency spectrums, hawking vs CMB.

This might be a little elaborate, and I haven’t thought about it further in over a year as to whether it would even work, but thought I’d share.

9. February 19, 2014 5:27 pm

JS, congratulations on hitting the bigtime, not merely a cite but a whole profile on RJLs blog. did you get past the 1k total comments mark and win this prize? 😛 (if so I have only a little less than 1k to go :shock:) ps you dont have a blog yet do you? you could start just by putting together all your greatest comments on other blogs, wink 😛
ps did anyone notice the most famous bloggers never comment on anyone elses blogs? 😦 … reminds me of mathoverflow & stackexchange where the highest rep users ask the fewest questions… 😕

February 21, 2014 5:31 pm

Bill Thurston’s high-rated MathOverflow question Thinking and Explaining shows us that mathematical luminaries *sometimes* ask *wonderful* questions!

• February 21, 2014 5:37 pm

ah, sometimes luminaries ask the most interesting questions! therefore would like to see stackexchange mechanisms that encourage the high-rep users into asking more questions. strangely the site seems to support their avoiding asking questions. this also reminds me of many of John Brockmans books. they’re huge compilations of Scientists Asking Questions. he’s been cranking them out like crazy for years now and I cant even keep up [even though they’re all quite fascinating]…. its sort of like a literary TED society….