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Hot Attraction

February 5, 2018

Forces acting at a distance have been commonplace in physics for hundreds of years, and because of their familiarity, they have lost their air of mystery. Presently, these forces are viewed as the consequence of a mediating field that carries energy and momentum across space. charges and magnets interact with the electromagnetic field and change it, thus producing the forces that we see. So, these mysterious forces have been replaced by the mystery of the field. It's "turtles all the way down."

Pliny the Elder (23-79 A.D.), whom I mentioned in numerous articles, wrote about the mystery of magnetism in Book XXXVI of his Natural History.
A marmoribus degredienti ad reliquorum lapidum insignes naturas quis dubitet in primis magnetem occurrere? quid enim mirabilius aut qua in parte naturae maior inprobitas?[1]

Upon quitting the marbles to pass on to the other more remarkable stones, who can for a moment doubt that the magnet will be the first to suggest itself? For what, in fact, is there endowed with more marvellous properties than this?[2]

Moving forward 400 years, St. Augustine of Hippo (354-430) expressed a similar amazement in his book, The City of God,
Magnetem lapidem nouimus mirabilem ferri esse raptorem; quod cum primum uidi, uehementer inhorrui. Quippe cernebam a lapide ferreum anulum raptum atque suspensum; deinde tamquam ferro, quod rapuerat, uim dedisset suam communemque fecisset, idem anulus alteri admotus est eundemque suspendit, atque ut ille prior lapidi, sic alter anulus priori anulo cohaerebat; accessit eodem modo tertius, accessit et quartus; iamque sibi per mutua circulis nexis non implicatorum intrinsecus, sed extrinsecus adhaerentium quasi catena pependerat anulorum. Quis istam uirtutem lapidis non stuperet, quae illi non solum inerat, uerum etiam per tot suspensa transibat et inuisibilibus ea uinculis subligabat?

We know that the lodestone has a wonderful power of attracting iron. When I first saw it I was thunderstruck, for I saw an iron ring attracted and suspended by the stone; and then, as if it had communicated its own property to the iron it attracted, and had made it a substance like itself, this ring was put near another, and lifted it up; and as the first ring clung to the magnet, so did the second ring to the first. A third and a fourth were similarly added, so that there hung from the stone a kind of chain of rings, with their hoops connected, not interlinking, but attached together by their outer surface. Who would not be amazed at this virtue of the stone, subsisting as it does not only in itself, but transmitted through so many suspended rings, and binding them together by invisible links?
Figure caption

St. Augustine of Hippo (354-430) was a Christian theologian and philosopher and the bishop of Hippo Regius in North Africa. His writings were important enough to have him declared a Doctor of the Church, and a saint whose feast day is August 28, the day of his death.

Augustine had a dim view of astrology, which was a respected science of his era.

(Circa 1472-1473 portrait of St. Augustine of Hippo (354-430), tempera on panel, by Antonello da Messina (1430–1479), sited at the Galleria Regionale della Sicilia, via Wikimedia Commons)

As we fast-forward more than a millennium, we find that action at a distance is still considered to be a mystery. As Isaac Newton (1642-1727) wrote concerning gravity in a letter to Richard Bentley,
It is inconceivable that inanimate brute Matter, should, without the mediation of something else, which is not material, operate on and affect other Matter without mutual Contact, as it must be, if Gravitation in the sense of Epicurus, be essential and inherent in it. And this is one Reason why I desired you would not ascribe innate Gravity to me. That Gravity should be innate, inherent and essential to Matter so that one Body may act upon another at a Distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed, from one to another, is to me so great an Absurdity, that I believe that no Man who has in philosophical Matters a competent Faculty of thinking, can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain Laws; but whether this Agent be material or immaterial, I have left for the Consideration of my Readers.[5]

As I wrote in a previous article (Depletion Attraction, March 7, 2011), even non-fundamental forces can be mysterious. There's an unusual attractive force between large particles called depletion attraction when they're in solution with smaller particles. Since two particles in solution can't occupy the same space at the same time, and one large particle can take the place of many smaller particles, surface effects become important, and the many small spheres filling the same volume as one larger sphere will have a larger surface area exposed to the solution.

Polymer scientists, Sho Asakura and Fumio Oosawa, discovered this force that's not a consequence of electrostatic attraction in 1958.[6] Small particles in solution can't access the space between closely spaced large particles, so they push the larger particles towards each other. The free energy change ΔF of this thermodynamic effect is described for elastic spheres by the simple equation,[7]
ΔF ≈ n kB T [1 + 3/2(D/d)]

in which D and d are the diameters of the larger and smaller spheres, T is temperature, kB is Boltzmann's constant, n is the volume fraction of small spheres, and (1-n) is the volume fraction of large spheres.

Figure caption

Heraclitus of Ephesus (c.535-c.475 BC) wrote that everything flows (παντα ρει), which might be paraphrased as everything moves.

This is shown by the Brownian motion of particles in solution, caused by another mysterious force discovered in 1827 by botanist, Robert Brown.

On an even smaller scale, there's the Zitterbewegung, the trembling motion of the position of electrons at an angular frequency of 2mc2/h, approximately 2.5465 x 1020 hertz, in which m, c, and h are respectively the electron mass, the speed of light, and the Planck constant.

(Modified Wikimedia Commons image showing computed Brownian motion at three hierarchical scales.)

Another mysterious force has been revealed in a recent open access paper in Nature Physics.[8-9] The hitherto unknown attraction of atoms to a hot blackbody radiator with a force about an order of magnitude greater than gravitation has been studied by an international team of physicists from the University of California (Berkeley, California), Lawrence Berkeley National Laboratory (Berkeley, California), the University of Glasgow (Glasgow, UK), the Medical University of Innsbruck (Innsbruck, Austria), and the University of Innsbruck (Innsbruck, Austria).[8]

The expected phenomenon is repulsion, not attraction. Bodies at any temperature above absolute zero emit radiation that exerts a small pressure on neighboring objects. However, a cesium atom at room temperature will intercept less than a single movement-inducing photon in a 100 million years, so this effect is negligible.[8] Atoms, however, will also interact coherently with the thermal electromagnetic field, and an attractive effect was conjectured a few years ago.[9] This is the non-coherent analog of the coherent laser beams used as optical tweezersoptical tweezers for trapping atoms.[9]

As you can imagine, measurement of such small forces takes a bit of experimental finesse.[10] To measure the attractive force of the blackbody radiation between a cesium atom and a heated, centimeter-sized, cylinder, the research team used atom interferometry.[8] The cesium atoms were laser-cooled to about 300 nanokelvin and launched upwards into free fall in an atomic fountain, and half of them reached 3.7 millimeter into the cylinder at their apex.[8-9] These interacted with the atoms not affected by the cylinder to cause a detected phase shift, allowing calculation of the attractive force.[9]

Attraction experiment

Experimental concept (left) and the experimental apparatus (right). In the right image, the shiny tungsten cylinder can be seen at top through the vacuum chamber window. (Left image and right image by Holger Müller, UC Berkeley.

It was found that the force, which was in good agreement with theory, scaled as the fourth power of the cylinder temperature over a large temperature range (see graph).[8] While this attraction is twenty times the gravitational attraction, it's still very small.[9] Says Victoria Xu, a co-author of the study and a graduate student in the UC Berkeley physics department,

"It's hard to find a scenario where this force would stand out... It is not clear it makes a significant effect anywhere. Yet... People think blackbody radiation is a classical concept in physics - it was a catalyst for starting the quantum mechanical revolution 100 years ago - but there are still cool things to learn about it."[9]

Acceleration as a function of temperature

Acceleration of the cesium atoms as a function of the temperature of the cylinder, showing a fourth power temperature-dependence. The data points are the averages of 65 measurements.

(Created using Inkscape from data in ref. 8.[8])

While the effect is small, correction for it might be needed in using high precision atom interferometers in searches for dark matter and dark energy, and gravitational wave detection using lab-scale instruments instead of kilometer-long interferometers such as LIGO.[8-9] This research was funded by the David and Lucile Packard Foundation, the National Science Foundation, the Defense Advanced Research Projects Agency, and the National Aeronautics and Space Administration.[9]


  1. Pliny the Elder: the Natural History, Book XXVI, from Bill Thayer's Penelope Web Site at the University of Chicago.
  2. Pliny the Elder, The Natural History, Book XXXVI. The Natural History Of Stones, Chap. 25, The Magnet: Three Remedies, English Translation by John Bostock and H.T. Riley, Project Perseus Web Site at Tufts University.
  3. Aurelius Augustinus, De civitate Dei, Liber XXI, pp. 412-426, via Wikisource.
  4. St. Augustine's City of God and Christian Doctrine, Chapter 4, Examples from Nature Proving that Bodies May Remain Unconsumed and Alive in Fire, Christian Classics Ethereal Library.
  5. Isaac Newton, Letter III from "Four letters from Isaac Newton to doctor Bentley, containing some Arguments in Proof of a Deity," 1756, p. 25f., via Google Books.. Also at The Newton Project.
  6. Sho Asakura and Fumio Oosawa, "Interaction between particles suspended in solutions of macromolecules," Journal of Polymer Science, vol. 33, no. 126 (December, 1958), pp. 183-192.
  7. Davide Marenduzzo, Kieran Finan and Peter R. Cook, "The depletion attraction: an underappreciated force driving cellular organization," J Cell Biol., VOL. 175, NO. 5 (December 4, 2006), PP. 681-686
  8. Philipp Haslinger, Matt Jaffe, Victoria Xu, Osip Schwartz, Matthias Sonnleitner, Monika Ritsch-Marte, Helmut Ritsch, and Holger Müller, "Attractive force on atoms due to blackbody radiation," Nature Physics (December 4, 2017), doi:10.1038/s41567-017-0004-9. This is an open-access paper with a PDF file available here.
  9. Robert Sanders, "Hot bodies are attractive," University of California - Berkeley Press Release, December 8, 2017.
  10. Interestingly, finesse is also an optical term used to describe a Fabry–Pérot interferometer.

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