Hypothesis: Brownian Motion can strip artifical anthrax coating

March 19, 2010

Hypothesis: Brownian Motion can strip artifical anthrax coating

The following is a hypothesis to try to explain how anthrax spores with an artificial coating at the time of the anthrax mailings in 2001 may have lost their outer coating.

Coated individual spores have low drag and low mass compared to clumped uncoated spores that have high drag and high mass.  The lower drag of artificially coated spores results in a higher diffusion coefficient for Brownian motion for these artificially coated spores.

Coated individual spores will thus have a higher mean for the velocity distribution from Brownian motion and a higher standard deviation of velocity.  Thus individual coated spores will experience a tail of much higher kinetic energy and momentum than uncoated spores especially if the latter are clumped.

The higher velocity distribution from Brownian motion and whatever else is impinging the spores will over time subject the outer coating of treated spores to experience collisions of much higher kinetic energy as well as spread out over a wider range of energy.

The binding of the outer coating to the spore itself and to silicon and whatever else is inside the spore will thus be subject to a greater stress including those that may find any particular resonances or weaknesses.  This need only find and enlarge holes and cracks
in the outer artificial coating, which was likely never a perfect geometric form in the first place.

Nature did not evolve to preserve such artificial coatings for a long period.  The natural spores themselves experience a low velocity distribution from Brownian motion and
they have evolved to endure this.  But the artificial coating has not evolved from anything and does not inherently need to be stable under the effect of Brownian motion.

Its quite reasonable to believe that the effect of the higher velocity distribution of the artifically coated spores will eventually widen holes and cracks through collisions of coated spores at high velocity in head on collisions until the artificial coating is gone and the spores acquire a low velocity distribution as natural spores have.  Thus over time the artifically coated spores lose the artificial coating.  Silicon is left inside the spores because once the outer coating is stripped, the spores have high drag and can clump so that their velocity distribution falls to that of normal spores. In fact, the additional internal mass simply helps to lower the velocity distribution thus adding to the stability of the spore.

Artificially coated spores with a high mean and standard deviation of velocity together with natural spores with low mean and low standard deviation of velocity from Brownian motion are not a stable equilibrium.  Over time the artificially coated spores transition
to uncoated natural spores.

Irradiation of spores will combine with the effect of Brownian motion as well as the treatment by TEM to subject artificially coated individual spores to a wide range of velocities and interaction energies. Subjecting artificially coated spores that have experienced months or years of the effects of Brownian motion to irradiation and TEM will tend to cover an even wider range of energy impacts and finish off the possibly tenuous remaining binding of the artificial coating to the spore and whatever is inside the spore.  Collisions of coated spores from Brownian motion then have an enhanced ability
to finish the job of stripping the artificial outer coating.  What is left is natural spores on the outside with whatever they contain of silicon and other elements on the inside.




Irradiation of the spores before analysis by Sandia:




How does irradiation kill anthrax?
Irradiation kills anthrax by shattering its DNA and other cellular components. The process for irradiating mail is the same process used to sterilize medical equipment.

During irradiation, an intense stream of electrons (or x-rays if x-ray technology is used) strikes the mail and any anthrax spores it may contain. The radiation dose is very high, about 56 kilograys of radiation, which is approximately 2 million times more than a chest x-ray.


The photons which make up visible light have energies of 270–520 yJ, equivalent to 160–310 kJ/mol, the strength of weaker chemical bonds.








Brownian motion

In the micron range of particles there is Brownian motion.  Spores are 1 to 3 microns in length and one micron in width.  The original observations of Brown were themselves from living things c. 1820 and his equipment was obviously much weaker and so he likely couldn’t see individual spores of bacillus but instead larger objects, or in any case not smaller.
D = k_B T/b

b linear drag coefficient

In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas).

sqrt(2Dt) = sigma

(Its really the velocity distribution we are interested in, not position.)
The silicon coating decreases the drag b.  Thus it increases D and thus increases sigma. So what happens is that the spores coated with silicon have a high velocity from the brownian motion collisions.  This means they are having collisions at high velocity until the coating is knocked off.  what is left is under the spore coat.




Ken Alibek: Of course they are WMD. The shelf life of these nerve gasses and chemical weapons. These are chemical weapons and they are WMD. The shelf life would be years.







Search silicon oxide “binding energy” eV

weaponized anthrax “shelf life”

bacillus spore coat exosporium

irradiated anthrax Michael Sandia

silicone polymer structure

silicon coating anthrax “Brownian Motion”

irradiation anthrax







Recent silicon coating discussion in comments at Meryl Nass


and at Case Closed


The outer artificial coating need only be good enough to last a limited period in this instance.  It can have holes and cracks in itself.  It can be loosely bound to the spore or to silicon inside the spore.  Its only enough for the Brownian Motion to produce a velocity distribution that can find and widen the cracks and holes and loose binding to the spore and inside silicon.

The artificial coating gives the treated spore a low drag and thus high mean and standard deviation of velocity from Brownian motion and the randomization of its velocity.  Head on collisions of artificially coated molecules at the upper end of the velocity distribution need only break, crack or widen the holes and cracks and loose binding to the spore and inner silicon to break off the outer artificial coating.

The remaining natural coated spore then retains inside it the artificial silicon but now has a high drag and thus low velocity mean and low velocity standard deviation.  It is thus within the range of velocity distributions from Brownian motion that spores have evolved to survive.

It is unstable to have two different velocity distributions of spores, one artificially coated and one natural.  Over time the high velocity distribution of artificially coated spores will strip the artificial coating by finding its weak points and concentrating the energy of two spores on the cracks and weak links and holes until the artificial coating is striped off and the natural spore with excess silicon inside is left.

This Brownian motion hypothesis thus reconciles initial observations of highly energetic spores in the lab and later observations of no artificial outer coating but silicon left inside.  Brownian motion in the velocity distribution of low drag high velocity artificially coated spores plus time leads to the striping of the artificial coating but leaving silicon inside the spore.   This links the initial lab observations under microscopes of energetic spores and the Senate office buildings being closed and the later observations of no artificial coating of the spores and high silicon inside them.

==Short summary comment left at Meryl Nass blog

The link below considers a lengthy hypothesis to explain how Brownian motion could have striped off an artificial coating of the anthrax spores leaving silicon inside them.

In a nutshell, an artificial coating would produce a low drag coefficient on the coated spore.  This would lead to a high diffusion coefficient and a high mean and standard deviation of velocity of the artificially coated spores by a random walk diffusion process in the velocity of the spores.

Some artificially coated spores would have higher velocities from the combined effect of high mean and standard deviation in velocity.  When they collided head on, they would widen cracks and holes.  The original outer coating may have had its own flaws plus only weakly been bound to the spore or to silicon inside the spore coat.  Over time, the collisions would weaken the bonds.

When the artificial coating is stripped, the drag coefficient goes up and the spore acts like a normal spore with low velocity mean and standard deviation from Brownian motion.  These spores are then stable. But silicon and other elements inside them are trapped and stay in them.

This hypothesis and mechanism reconciles the initial lab observations of high velocity spores with the later observation of silicon inside the spores but no artificial coating outside them.


Also at



Two distributions of spore velocity in the same sample are not stable as a general principle of both quantum mechanics and random processes.  The artificially coated spores can transition to low velocity spores by losing the artificial coating.

This is a one way transition.  Thus over time, we expect to see the artificial coating that causes a high velocity distribution to be lost leaving normal spores but still retaining their extra silicon inside.

The high velocity distribution is created by the artificial coating having a low drag coefficient and thus a high diffusion coefficient and thus a high mean of velocity and a high standard deviation of velocity.   Over time this high velocity, high energy distribution will decay to the normal low velocity mean and standard deviation by the loss of the artificial coat.  The extra internal silicon is then left over as observed.


In October 2001, the initial lab observations were of high velocity spores, unlike what the observers had seen before of other spores. This is direct evidence of the high velocity distribution from Brownian motion in the spores in October 2001.   The high velocity of the spores they saw in the test tube and plates in October 2001 could only come from Brownian motion.  It shows the drag coefficient was very low, so the velocity distribution of the spores was high.


The exosporium of the spore, the very outside, is not firm and rigid. There is no firm structure to tie onto to resist the high velocity collisions.  Potholes and cracks will develop and widen until the artificial covering is stripped off.

The spore will expand when it becomes a vegetative cell.  We know that this happened, since people died from the anthrax.  This shows the spore was able to break any artificial covering that was around it.  This shows, if there was an artificial covering, it was not a rigid structure encasing the spores in unbreakable bonds.  Instead it shows the typical forces of spore expansion were sufficient to break the artificial covering.

Any artificial covering designed to weaponize has to be a weak one so that the spore can expand and break it and become a vegetative cell.  Thus an artificial covering to reduce the drag coefficient on the outside will be loosely bound to the exosporium and will not be a rigid covering that can’t be broken by the forces the spore can exert by growing.


They saw high velocity spore motion in the test tube and on plates in October 2001.  This is direct observation of the high velocity distribution of Brownian motion.   In a sense, the high velocity distribution of the spores observed directly in October 2001 by examination under the microscope is sufficient itself to demonstrate or show a physically different state of the Senate spores from normal spores.  This difference is in having a low drag coefficient and high velocity distribution.  The low drag coefficient implies dispersal.  The high velocity distribution observed directly was the direct observation of dispersal.

This high velocity distribution of spores observed directly under the microscope is in effect a direct observation of a low drag coefficient of the spores.  Thus it shows their dispersal tendency was higher.  This is most easily explained by an artificial covering.  But such an artificial covering has nothing on the exosporium to grab onto with unbreakable bonds.  Instead it will have a loose connection to the spore and possibly to silicon below the exosporium in the spore coat.

==Dxer Comment at Case Closed

DXer said

March 20, 2010 at 9:27 am


I recommend you read the excellent MICROBIAL FORENSICS, Bruce Budowie editor, available for free through your public library’s interlibrary loan.

==Reply to Dxer at Case Closed

The high velocity of the Senate spores were observed directly under the microscope in October and November 2001.  The spores flew off the plate they said.

They have seen normal spores under the microscope.  So the observation of high velocity spores was a scientifically valid observation.

The spores under the microscope were showing a velocity distribution in all directions not one direction.  That is what Brownian motion is, a random walk in all directions.

“Einstein predicted that Brownian motion of a particle in a fluid at a thermodynamic temperature T  is characterized by a diffusion coefficient  D = kBT / b, where kB is Boltzmann’s constant  and b is the linear drag coefficient on the particle ”


In Einstein’s 1905 article he looked at displacement directly.  So he did not have a random walk on the velocity.  That came later in the work of Ornstein and Uhlenbeck.

So in October 2001, the scientists saw a high velocity distribution of the spores.  This was not in one direction so it was not some em field in the lab.  Instead it showed that the drag coefficient of the spores was low.  The math is more complicated than the formula above, but essentially, the velocity distribution has a higher mean and standard deviation from the lower drag coefficient.  This is what they observed directly in October 2001.

The higher velocity distribution shows a lower drag coefficient.  That is either the embedded silicon alone or more likely a coating on the outside.  Such an artificial coating would thus mean that coated spores would have high velocity and uncoated ones low velocity.  This is not an equilibrium.  So over time the coating gets knocked off, leaving the silicon in the spore coat trapped.

The outer coating would not have much to hold onto in the spore.  The exposporium of the spore is not a rigid structure suitable for resisting repeated bombardments from high velocity collisions.  Binding to the silicon inside would be tenuous since it was removed spatially from the outside.  Moreover, any artificial covering had to be designed to break when the spore grew back into a vegetative cell which involves expansion.  We know that happened, since people died from the anthrax.

Thus the Brownian motion in velocity mechanism reconciles the direct observation of the high velocity distribution of the spores in October 2001 and the latter observation of no spore coat but silicon still trapped inside the spore coat below the exosporium.



This is a mathematical discussion of the Ornstein Uhlenbeck approach.  It shows that the variance of the velocity distribution is inversely related to the frictional drag coefficient and proportional to the variance of the instantaneous Brownian motion and a damping factor from the mean reversion implied by the frictional drag effect.  See around slide 10 and 11 for the final formula.  See slides 3 and 4 for the set up in terms of a drag coefficient.  Low drag coefficient means a low tendency of the velocity to go back to its target, in this setup zero.  A high drag coefficient means a rapid tendency for the velocity to fall.

Coating the outside of the spore to aid dispersion means in effect coating it to lower the drag coefficient.  Its the mathematical definition relative to the formulas of a random walk in the velocity of the Ornstein Uhlenbeck type.

The high velocity of the spores from Senate anthrax was observed directly in the lab under the microscope in 2001.  So this is a direct observation of a low drag coefficient through the OU type formulas as exhibited in the above link.


In the formula discussion the velocity is a signed quantity.  So positive velocity along the x axis means moving to higher x values.  Here the mean of the velocity is zero since there is no preference for right over left, or up v down.

If we define speed as the absolute value of velocity, then the speed will not have a mean of zero.  As the variance of the velocity distribution increases, the mean of the speed increases as well.  Thus a low drag coefficient means the mean and variance of the speed both go up.  This means the mean and variance of the speed of the spore are higher the lower the drag coefficient.

So an artificial coating increases the mean and variance of the speed of the spores.  This shows up under the slide as the effect that the spores seem to be moving fast even if its in different directions.  The higher variance of velocity from the lower drag coefficient thus ends up increasing the collision kinetic energy between coated spores, which are sometimes head on, i.e. they have opposite direction of velocity.

Over time these collisions find the weaknesses, joins, holes, cracks, and loose bonds of the outer coating to the spore.  Thus the outer coating becomes full of pot holes and cracks until it breaks off.

In equilibrium, the outer coating will be gone from the spores and all the spores will have high drag coefficient and be in the same distribution of low speed, i.e. low variance of velocity around a mean velocity of zero. This is exactly what the formulas linked to show.


Search Ornstein Uhlenbeck velocity distribution.  Or Brownian motion velocity distribution.

Some derivations from a more elementary starting point are given here:


Note the orientation is to diffusion on the displacement.  The original OU paper did a velocity distribution and that is gone through at the link cited above.

==Further comment at Meryl Nass in rebuttal to the No of Dxer.

The formulas for the velocity distribution of a spore under from random collisions in a media of smaller particles is given here:


I apologize for the unsightly link, but its the best I could find.

The formulas show that the variance of the velocity is inverse proportional to the drag coefficient.  The drag coefficient just means the tendency of the velocity to revert back to zero from friction.

F = – gamma m v

where m is the mass of the spore, gamma is the drag coefficient, and v is the velocity.  There is an additional random forcing term from random collisions with molecules.

When gamma is low, the drag is low, i.e. friction is low.  In this case, the variance of signed velocity is high.  In that case, we get some very high velocities compared to a spore which has a high drag coefficient gamma.

In October 2001, the labs directly observed high velocity movements of the spores under the microscope.  The spores flew off the slides.  This was observing the Brownian motion of the spores.  The original observations by Brown were on pollen.  Brown was a botanist.

The high velocity of the spores in October 2001 under the microscope was not due to em fields since it had no particular direction.  It could only be from Brownian motion.  Which means they directly observed the velocity distribution as high compared to normal spores they were familiar with.  This was equivalent to directly observing the drag coefficient as low.

Unless silicon in the coat causes this, there was an outer coating. In either case, the spores had a high velocity distribution from Brownian motion.  That is just fancy math talk for saying they dispersed.  The math of dispersion is the formulas of the velocity distribution under Brownian motion at the above link.

Since coated spores have a higher velocity then uncoated, over time, coated spores will suffer higher velocity collisions.  This will widen cracks and holes just like pot holes in a road.  Eventually, the coating is knocked off leaving the silicon inside the coat still there.  The uncoated particles have a high drag coefficient like normal spores and thus a low velocity distribution.

==Further reply to a comment by Dxer at Case Closed

High velocity follows from low drag coefficient. That is the formula.  We know the spores have velocity as seen under the microscope in October 2001 from Brownian motion because it was in all directions at once.

They observed a high velocity compared to normal spores.  That shows a low drag coefficient through the formula of Ornstein and Uhlenbeck for the variance of velocity in terms of the drag coefficient.  They are inverse.

Thus the drag coefficient was low for Senate anthrax compared to normal anthrax spores they had seen before under the microscope.  This was observed.

The drag coefficient being low means low friction.  A means for the drag coefficient to be low is an outer coating that doesn’t stick to whatever is around.  Thus the high velocity of the spores observed under the microscope compared to normal spores is evidence of an outer coating that reduced the drag coefficient.

The outer coating may or may not have been silicon although it seems likely.  The outer coating had to bind to something on the spore.  That could include the exosporium and the silicon in the coat.

Brownian motion of spores and the 1930 formula of Ornstein Uhlenbeck for the velocity distribution of spores in terms of a friction drag coefficient is  a basic part of spore science.  The energetic motion of the spores they saw under the microscope was Brownian motion exhibiting the OU formula for the velocity distribution.  Einstein won the Nobel for his simpler formula of Brownian motion.  Uhlenbeck won for his work with spin.

Having coated spores with a high velocity distribution from a low drag coefficient alongside spores that are uncoated with low velocity from a high drag coefficient will then be subject to the forces discussed which will tend to strip away the outside coating until there is equilibrium and all spores have high drag coefficient and low velocity distribution.


In October-November 2001 they saw under the microscope high velocity spores compared to normal spores.  The velocity came from Brownian motion in the Ornstein Uhlenbeck mode of analysis.  Thus they observed a low drag coefficient of the spores in October 2001.  Thus they observed something causing that low drag coefficient.  That would seem to imply a coating that lowered the drag coefficient.  So they observed a coating in October November 2001 appears to be what they observed from the high velocity.


The Ornstein Uhlenbeck velocity variance formula equates a high velocity to a low drag coefficient.  A low drag coefficient appears to best equate to a coating that lowers the drag coefficient.  Thus high velocity is equated to a coating.  Thus by observing the high velocity in October November 2001 under the microscope they observed a coating through the Ornstein Uhlenbeck math of Brownian motion.

The Sandia observations were also based on using formulas and indirect effects.  Thus Sandia observed no coating from its indirect analysis that came later and the microscopic examination of high velocity Brownian motion observed a coating in October November 2001.  The reconciliation is that the high velocity Brownian motion will eventually strip away the coating so that the spores are back to low velocity uncoated spores.  That is what Sandia saw.  So both sets of observations of the coating were indirect through math formulas.  They are reconciled through the high velocity Brownian motion itself stripping the coating over time to achieve equilibrium with low velocity uncoated spores.


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