Sorry.

For the record.

The.

Start of it.

And you go to war.

Thank you very much it means
pleasure meeting the interesting

faculty here and
the wonderful research that is going on so

I am going to tell you about
causing the forces and

some suggestions that causing the forces
can be used to levitate objects

and so
the introduction is some basic idea as

a recap of what causing the forces
both in the quantum context for

actuations are important and
where the need and

suggestion of the possibility of making
Casimir forces rather than attractive

repulsive comes from and
some ideas about whether or

not these kinds of repulsion
proposals are feasible and

ideal and
with some brief discussion of dynamical

Casimir Effect but
back to the original Casimir Effect

as proposed by Henry Casimir in one
thousand nine hundred eighty eight

he said that if you have two mirrors
the modes of the electromagnetic field

between them are going to be quantized so
that you will have multi purpose of.

A relationship between They've lent and
the separation and each one

of these modes will have a characteristic
frequency and if you think of them as

harmonic oscillator because of the zero
point two Asians of the electromagnetic

field you would assign each borrow make
over two to each one of these modes and.

And what Kasimir found was that the sum
of all of these eight ball makers is

naturally infinite but interestingly
if you take the derivative of

that infinity you will get a finite force.

The force naturally has to be
extensive proportional to the area

it is quantum in origin so
it should be proportional to a four C.

comes from the electromagnetic field so
this should be there and

that's it so then you ask well that
doesn't have the correct time mentions of

course it does if you divide by
four powers of historians and so

up to a numerical factor the Casmir
calculated pi squared over two hundred

forty you know everything about what this
force should be based on dimensional

arguments for spare unit area is
equivalent to a pressure and if you put

numbers you find that this pressure is of
the order of a fraction of an atmosphere

if you go to separations that are of
the order of a fraction of a micro.

So.

This very idea.

For scription of Casimir was
generalized later on by Lipschitz

not to think about ideal mirrors but
metallic plates and

he could show how the result was
modified by having dielectric plate and

how actually discussing
the force continuously

in terror police when surely becoming the
band there was for such short distances.

Because of the smallest of this
Force One had to wait until

late one thousand nine hundred ninety S.

so that I to make force microscopy
provide the juice to measure

forces at this of my concept her
relations with sufficient accuracy that

the theory could be confronted with
the experiment and starting with.

Lamb row and later on with more here
Dean and Roy The Casimir force was.

Measured and compared to tear.

Only at the level of a few percent there
is agreement Interestingly there is

a persistence difference of the order of
a few percent that has kept the theorists

an experimental is in the field busy
since and is not yet resolved but.

Applications of the force come whenever
you talk about micro electro mechanical

devices that is devices that
have to pass current so

they have to be made of metals and
you want to have them at the level

of Micron scale which is where I said
these forces should be important answer if

they are mechanical devices you have to
worry about what this Casimir force does

to their stability and
one of the discussions

is that since the sport is
an attractive force short distances

the force becomes actually stronger in
a star short distances and it could lead

to a mode of failure in the various
mechanical components stick to each other.

So this has motivated the search for
possibility of making Casimir

interaction either reduced or potentially
even better making it repulsive and

that is subject to come back to but

before going to that I will
mention that there is another

analogue of Kazimierz when you think
about the Casimir force as due to quantum

fluctuations of the electromagnetic field
in the space between two plates and

how those fluctuations are constrained
by the bounding plates

you can ask Well I know that there
are also lots of thermal fluctuations and

would term all fluctuations confined and
constrained by two plates

lead to simular Casimir
fluctuation in use force and

the answer is yes but typically do
those forces are very short grain.

Because the presence of a boundary
only is felt by the gas over for

a few correlations lends so

in order to have the kind of long range
force that Kazimierz had predicted for

electromagnetism like electromagnetism
you need to have a theory with

infinity correlation Lent which for
classical systems you can only find

that special points such as the critical
point of political gas system or

did the mixing point of an old
water mixture and be sure and

vision pointed out that if you
happen to be at such a point then

you can say that due to terminal for
actuations there is a modification

to the free energy of pint
size scaling that is due to

terrible fluctuations so it has to be
proportional to K.T. like the Casimir

force it has to be proportional to area
and again to make it dimension less

you have to divide by appropriate poverty
of the separation between the plates.

Now generally This gets more due elated
by a function of separation divided

by the correlation lent by the point where
the correlation land goes to infinity

this becomes just a pure number just like
that pi squared over two hundred and

forty of Casimir and essentially
you have this regime of universal

forces again and the reason for
universalities because of the long

correlations length you are averaging
over many things and the details go away.

This critical Casimir force of turmoil for
actuations was actually.

The experimental E ten years after
the quantum version by a group.

And basically what they had was
a co-leader particularly in a fluid.

That was feeling kind of Casimir
like interaction rather than play

two plates between a sphere and
a plate to the surface and

this ball was in all of water mixture so

she was the one that I had indicated over
here and the human the temperature to

approach the critical point at which
the correlation lent went to infinity and

by looking at how of for
a way this particle was

floating they could figure out what the
potential of the interaction was and what

they could sure was that the potential of
interaction indicated by these curves very

much depends on how close you were to the
critical point and by the time you reached

the critical point the interaction
that you were generated through this

modified clock creations was essentially
becoming Pavol law an infinite ridged.

So the answer is that basically
you can have these term

are fluctuations to become long range if
the correlation length is sufficiently

large now in connection to what I was
saying before regarding attractive or

repulsive it turns out that this force
that is acting between the sphere and

the plate can be made both repulsive and

attractive in the way that you can
go from one to the other is to quote

the two surfaces to either be
the same idea or both hydrophobic or

hydrophilic or to be different and
if one of them is hydrophobic and

the other is hydrophilic then rather than
attraction you get every politician and

indeed by appropriate
coating you can sort of

make these particles gather
into these channels and

reverse their belief so you change the
temperature and they can either form these

nice columns when you are at a critical
point or they become randomized so.

The story is that certainly the Terra
modern version of the Casimir force

can be both attractive repulsive
depending on whether the boundaries of

the two surfaces that you are looking
at are the same or different so

the question is having stablished this for
the thermal Casimir force

can we make the quantum mechanical
version to also be repulsive

answer the lesson was that
what you need to do is to make

the boundaries sufficiently distinct and
different from each other and

you can indeed do that for
the case of the quantum causing your force

by the following set up
if you have a medium

in which the dielectric
constant of the medium is

intermediate between the two surfaces so
that at one of the surfaces

you are going from dilute to dense in
the other case you are going from.

Thence to dilute.

Then the boundary conditions
the way that right reflects

is sufficiently different that
you will get repulsion and

this actually is one way of thinking
a very thinking of a very well known or

survey showing that is he knew him
climbing walls of container such as

a glass because they dielectric constant
of helium is certainly larger than air but

it is smaller than the class so
this is a situation where the boundary

conditions of the electromagnetic
field the two sides of this.

Helium liquid boundary are different and
so there is a repulsive force that wants

to make that boundary larger and that
would be one way of accounting for this.

BALL That feeling that creeps
up the glass plates also.

Experiment that I was shown showing
you here was performed by the group of

capacitor and
they had surfaces of gold and

silica and in between them
they had the oil drum by and

then seen that as intermediate
dielectric constant and

they could actually float this
gold because of these repulsive.

Casimir forces if you like.

But.

That kind of situation would

be impractical if you
are building one of these micro.

Devices because you don't want to put oil.

Covering all of your device so
it would be ideal

if somehow we could achieve
a repulsion across vacuum.

And possibilities of that were
originally pointed out by

boy here from two ready called
perspective he showed that if you do

just a purely mathematical calculation of
two boundaries one of them is a perfect

metal in the sense that you put Epsilon
the dielectric constant going to infinity

and the other is a perfect
diamagnetic in that perfect.

I no longer fit the emission rather than
epsilon going to infinity you make me you

going to infinity the two boundaries would
be sufficiently different that across

vacuum you would see the analog
of a Casimir repulsion and

now the problem is that most of
the material that we have around

us have values of music that
are of the order of one so

that does not work but
we have to know the Billy T.

to design materials called
metamaterials in which

effectively you could endowed them
with different responses to a.

Actually can magnetic fields so for
example if you take a silly coin and

print on it gold circuits such as the ones

that are indicated over here you can see
that if you try to pass a magnetic field

you will generate current that would
oppose this magnetic field and

so this metal materials that
have been proposed as a means of

achieving cloaking for example have
been suggested as being candidates for

achieving this boy here mechanism and
giving repulsion So

this article says it sounds
like a science fiction joke but

it isn't what you get when you turn
an invisibility cloak on it's side

a flying carpet so
these metal materials are supposed to be

good at all kinds of things so
we'll see if that's the case.

Well that was one way or suggestion for

how you can achieve repulsive Casimir
forces across vacuum another story

has to do which Jonah three and
shape and for that I will tell you.

Another story in which
Casimir played the party.

So this goes back to trying to figure
out a classic called model for

the electron as a ball of charge
each the problem with the ball of

charge is classically is that
it has a self repulsion of

squared over all our answer clearly
you can't set our going to zero so

that you have a point particle without
having to deal with this large capacity

for energy now Kazimierz said
well if I think of this ball

as a metallic spear and the modes of
the electromagnetic field have to

be modified by going to zero or
this we're this will cause it's.

Similar modification to what I had seen
for parallel plates I don't know how to

do it calc to how do the calculation but
I can't estimate how it should look like

it has to go again be proportional to
each bar it has to be proportional to C.

and dimensionally the only
way that I can make.

Something that has dimensions of
energies to multiply each bar see

by an inverse Lent and so there's
a radius of this here must appear here.

So he said that maybe there is some kind
of a Casimir attraction that modifies

the electrostatic repulsion and stab
Eliza's the electron So if A is chosen so

that this net thing is zero then I
would have a model of the electron and

as a bonus I would have captured for the
value of the fine structure constant this

so there was this proposal to calculate
this although he couldn't do the job

properly well many years later at
Harvard the graduate student while

Boyer was a graduate student he sat down
and calculate all of the modes etc and

calculated what this parameter ABERS and
surprisingly he found that he was negative

so this picture does not work
however this observation

then initiated a whole set of other things
about three positive Casimir forces

because an A that is negative means
that essentially the net effect

of these quantum fluctuations rather
than trying to force this for

years to become smaller is something
that wants to make the spear bigger So

this looks like there is some kind
of every policy of pressure so

the suggestion was that maybe if
you were to cut this fear in half

the two sides of this fear
would Rick Perry sure there and

saw all of you really need to do is
to play be German three in order

to get your positive causing
the forces and the simular orbit.

The ration was made or the calculations
were easier you don't have to

do this we're you can do hyper
you can do parallel of pipe and

with some ratio of the lens scaling
of would see this and then there were

proposals of various devices that
would work based on this report.

However.

We could show that if you had more.

Experimentally accessible Juma three
in which we put a piston that was

movable in the middle of this
parallel parallel look Piper and

added up the energies of the two sides we
would find that this piece stone would

be attracted to one side or the other it
wouldn't repulsion you wouldn't be hanging

in the middle and then there was
a theorem that was proven by clique and

coworker that if you have two objects
that are mirror symmetric they must in

fact attract the sure they're due to some.

Reflection positivity property of quantum
mechanics so a lot of these theorems.

Your own sort of violated and
threw out the suggestion

that by playing with the geometry
you can cause repulsive interactions

there is actually one case of a German
three that works imagine that you cut this

out of a metal plate and
you have a shape such as a bullet

this group showed that
the bullet would actually be.

Pushed away from the circle of this.

Circuit.

So given all of these issues.

There was some kind of uncertainty and
this uncertainty

reminded me of something simular
uncertainties that existed.

Few hundred years ago and
that was the question which is where or

not it is possible using electrostatic.

Forces to levitate something so

electrostatic forces certainly can be
attractive or repulsive so maybe we can

put some arrangement of plus and
minus charges that together can keep

something afloat and
I guess at the time of any sure.

Where your suggestions in this regard and
so

he proved the theorem that I really
like the first paragraph of the space or

if there are before the world by
various authors several memoirs which.

Embrace the subject of the present
communication that is levitation

there is Observateur in them
however much this agreement

of results which seem chiefly to
arise from the extreme lengths and

complexity of the investigations by
which those results are obtained

to avoid which as much as possible
there are tools are compelled to adopt

means of seem to fit cation
which are not always a priority.

Sufficiently approximative in the
following pages the subject will be found

and treated in a manner perfectly new and
direct and.

Basically what he proved
was the following.

That essentially if you have a situation
such as this where you want to maintain

a charge in equilibrium in the presence
of other things it could leave you on.

This charge is moving in
a potential that is set up by

all the other charges and electrostatic
potentials are subject to the.

Law plus the end of the potentially cause
to zero which means that potential if

it is stable in one direction so that
moving in one direction you have a restore

in force because the A plus in has to be
zero it must be of the form of the sad.

They are and should be unstable
in the other direction OK So

this immediately rules out levitating
with the electrostatics and

I want to show you that
least in one simple case

which by a few lines of algebra we
can sure the same to be true for

some kind of a fluctuation induced forces
this is not quite the Casimir force but

it is in the same spirit imagine
that you have a bunch of

objects that are charged neutrals
However within each of these

objects there are plus and minus charges
that can pop out and move around so

for example bags of and
I only solution is a very good

example of what these objects
look like now because of the.

Interactions between the local and
instantaneous charges there are average

fluctuation in used interaction
between all of these bodies and

the question is whether I can maintain
one of these bodies in stable

equilibrium in the presence of all
these other fluctuating charges but

how would I answer that rather than
having an energy because I have

things that are fluctuating I need to look
at the free energy which is octane by

taking the low bury them of a partition
function where all of the configurations

of these charges are included
weighted by the appropriate energy.

Part of this energy is the Coolum
interaction that I would have

between all of the charges
in the story and

then there will be all kinds of other
constraints that keep the charges.

Now the analog of law plus
enough electrostatics

in the law plus enough this free energy
should I make a change in the core of

the unit of this object and
by taking appropriate

deliberative to follow bury them which
is what the free energy is you can.

Very easily sure that this law class
in under one hundred is the average

of the law plus the end of this object
which is in fact zero because it's

cool on interaction and
then there is gets a correction due to

variance of the fluctuations
in the force and

the variance of the fluctuations
always is positive and so basically

this object is certainly
negative which means that you

are less stable so
in some sense fluctuations.

Even in the presence of a saddle allow you
to explore the vicinity of the saddle and

on average feel push you
in the unstable direction.

Now this is a few line proof we could
actually do an analog of this proof rather

than terrible fluctuations which was the
basis of the Boseman way that I was using

with full quantum mechanical fluctuations
except that the point a mechanical

calculation is much more difficult I'm
not going to present it to you but

the answer is that indeed the lock
last year of the electrostatic energy.

The fluctuation in use the analog of
the Casimir force that you have for

a bunch of objects is negative
as long as the objects can

be described by a dielectric constant
that changes the function of position and

frequency in arbitrary manner that
doesn't violate this that will it is of

materials and so
that immediately rules out being able

to use these metamaterials as
a way of levitated about it.

Now.

Of course every theorem is as
good as the conditions for

that theorem and
we know that indeed using optical

tweezers we can keep things
in levitation the reason for.

That is that we are not dealing
with Electra statics but

things that are changing as a function
of time and we know that it is possible

to levitate frogs and the reason for
that is that the frog is

made mostly of material such as water
that has diamagnetic properties and

magnetic properties are not part of the
construction of an shows to your own so

there are various ways of
still levitating things but

these theorems give you some kind
of constrains as to what is.

Not possible.

So now the question is.

How would we wire late this.

And one way of violating this
condition my assumption was that you

need to be in equilibrium so I showed
you did clear on that first valid for

the case of zero temperature but in
fact it's also a valley that the case is

a finite temperature as long as
you're in a collaborative but

you say if things are out of
the quality of your I can certainly

have repulsion so that if I have for
example a hot plate the hot plate

that would be radiating more photons
compared to the cold plate and

the pressure of radiation could
potentially keep the cold plate

afloat maybe that's why I
have a nice floating above.

Who knows but
the point is that if you look at

the pressure due to radiation it is
given by this there from Boseman law

it is proportional to the temperature
to the fourth power Where's

the attraction that I said that I mention
only has to be off the order of H.B.R. C.

over the to the fort So
you see that poor this to be valid.

As long as you are at a temperature
that is of the order for

room temperature you have
to go to distances that.

Or of the order of ten microns for
example and

at those distances The causing the force
in any case is too negligible to bother.

However it is also known that
a lot of things that we know

about different Boseman law are not
necessarily correct when you go

to very short distances there are things
known as near field effects so

let me less least one of those things
which is for example we say that

the amount of radiation that you have from
an object is proportional to its area

well if the object is sufficiently small
IT field properly proportional to its war

you it's essentially you will have lots of
atoms that are individually radiating and

we're used to thinking of black
body radiation as being completely

isotropic and not polarized but
if you have for example the Nano wire

then the radiation will be polarized
depending on you look at parallel to

the wire perpendicular to the buyer So
there are reasons to sort of not

think about this as being correct
answer the question is how does one

more generally discuss a situation
where you have a whole bunch of objects

that are locally in and could leave
the room a different temperatures but

the temperatures are different so there is
constant heat transfer between them etc.

Now this is essentially one.

Slide of theory debate to handle these
things was introduced by rich off in

one nine hundred fifty nine in something
that he called fluctuation our Q.B.

I like that name basically what he
said was that when we are thinking

about an object that is at some
temperature really there are all kinds of

fluctuations that are going in that object
and including among them our current flux.

Creations the average
currents will be zero but

the variance of the current
will be non-zero and

will be related to a combination
of how hot you are and

even if you go to zero temperature
you two quantum fluctuations So

essentially this expression is
able to give you fluctuations

in the current that you have in each body
depending on temperature also including

zero point three zero actuations and
it is really related only to

the imaginary part of the diet he can
stand that describes this material.

Now if you look at the system
then at some instant of time

you will see a bunch of current and
if you know the currents you can in

principle calculate an electric field
by using the green's function for

the shapes that I'm looking at relating
linearly the currents the electric

fields I say in principle you can
calculate the response and sort but

it's going to be a very difficult task
let's leave that for the time being.

The point is that because the average
current is zero the average electric

field is zero but the fluctuations of
the electric field the core variance

of the electric field will LOT be zero and
can be related to the core variances

of the current through the use of these
greens functions now once I know the core

variance of the electric field I'm set
I can calculate all kinds of things

because I can calculate the Poynting
vector that is related to each cross H.

would be essentially one
of these objects and

once I have the pointy vector I know where
the heat that he's going from one to

the other I can calculate this stress then
sort of months I have the stress tensor I

can calculate the force that
is acting on each body etc and

so using that you can answer
a number of things you can for eggs.

Calculate exactly for
the experimental situation for

people who looked at in the know why and

the analog of the black body
radiation from a nano wire and

sure that it has some strange properties
such as being polarized in some

particular direction and
again the amount of that is radiated

not necessarily being proportional
to the area of the surface but

proportional to war you mean the full
crossover care of it we can calculate

using this theory and
other very interesting observation is that

according to the classical things
that we teach if I have a hot and

cold object the radiative heat transfer
between them is simply proportional

to the difference of the fourth powers of
the temperatures between the two of them.

So a colleague of mine at MIT in two
thousand and nine said to test this by

looking at the heat transfer
between a sphere and a plate and

the results are plotted here as a function
of how close this fear is to the plate and

at four distances he gets the results
that can be calculated from this theory

and that's actually the straight line here
that does not go to zero but it is to one

but when you get to distances that are
fraction of a micron suddenly you can see

that the amount of heat that is
transferred goes up by several thousands.

And so this is an example of the violation
of this Stefan Boltzmann law and

very quickly if you ask why that is
is because men we are teaching and

calculating this quantity in our
courses we rely on propagating behaves

versus when you get to very short
distances the main mode of heat transfer

is through evanescent waves that tunnel
the energy if you like from one side.

First one other surface.

And similarly you can get
interesting results about forces and

forces between two microspheres for

example can be both attractive
repulsive if they are not at the same

temperature if they are at the same
temperature you have the usual one over D.

to the six man there was a fraction then
one of them is a different temperature at

high enough distances you will get there
repulsion and between the attractive

only positive poor poor there could
potentially be a point of stable.

And so basically this is
supposed to show that for

you we did a calculation where
tungsten sphere was levitated

on top of a surface heating this
year to one hundred degrees

is sufficient in principle to
keep it levitated above this fear

unless it cools down which means clue the
effect of cooling down because of cooling

down he eventually falls
down to the object so

basically the story here is that
a whole bunch of different.

Non-nuclear your mean the sense of
objects being at different temperatures

can be calculated using this.

Ditto for Mali's But I want to
jump to another surprising thing.

Which we can still do using
the ritual formalism which is a form

of non-equal Librium in which I don't
have objects at different temperature but

an object that is in motion so

imagine that you have a sphere a metal
sphere sitting inside in vacuum and

it is rotating by itself OK if
you say well angular momentum

is going to be conserved then this
object will continue to rotate forever.

Well the answer is that this object is I.

Actually moving in a sea of quantum
mechanical electromagnetic fluctuations

and potentially in the same
way that a sphere in

water will slow down this weird
will eventually slow down

but the interesting thing is
how it does that because.

One way to look at the is this object

has rotational symmetry so
an appropriate basis for

extra magnetic waves to consider are the
ones that are also characterized by.

I wrote a Chanel symmetry and
having some angular momentum M.

so I look at electromagnetic
fields outside the object

that have a character as far as
the angular dependence is concerned of

it to the I am Farai and they are rotating
with some frequency smaller Omega.

Now if the object is rotating
with a frequency big or

make up and I'm rotating with
the object I have now move and

sit on the frame that is moving with
this fear then from the perspective

of a sphere I see that is changed by this

rotation which means that effectively
the frequency that you see is

the stroboscopic Lee modified
between the outside and

the inside of servers by an amount
that is related to times big homie.

Interestingly the door which was
looking at this situation of

scattering of waves from
a rotating sphere and

you observe that if you are very in
the circumstance where Omega and

omega are prime different signs
will make of us positive but

will make a crime became negative
then if you scattered way

from this fear the amplitude of
the scattered wave was actually larger.

Than the incoming and
this is a phenomenon because super radius

essentially the wave on scattering get

some more energy extracting some energy
from the kinetic energy of rotation.

And now what we sure was that if this beer

is rotating by itself precisely
in the range of frequencies that

dovish predicted super gradients to
a care it spontaneously Emmett's

radiation so essentially the veil
that this sphere slows down is by

emitting waves in precisely
this range of frequencies and

you can figure out how rapidly
loses energy etc It's a very small

amount but
it is an interesting story to think about.

This is one example in the field of
dynamic causing your effects which

discusses situations where the plates that
Casimir was thinking rather than being

static are moving and one can sure that
if these surfaces are moving very rapidly

you can have circumstances in which you
create a photo nds and you lose energy and

so even if you have parallel plates moving
with respect to each other you have

a kind of friction that is going
on you have friction of vacuum.

But one thing that I want to conclude with
and let me see I do have a few minutes is.

The following that all of these forces
that I mentioned to you because even

your forces search for a arise from
some kind of underlying fluctuations and

the quantities that I have given
you are always the averages so

all of these forces certainly
also have fluctuations and

one can ask how big are the flock to
ations off the fluctuation induced force.

And probably the best place to see
it is a place where the average

forces erode so he can focus on
what the fluctuations are doing.

And so wanting that you can do
is you can take this we're not

the rotating sphere just a metal
sphere by itself put it in vacuum on

average there should be no force on it but
there should be fluctuations on the force

now this should remind you
of the coal oil particles so

if I were to put a quote particularly
in a fluid such as water there is no

net force on it because of symmetry but
because of the fluctuations of

the water molecules it
undergoes Brownian motion So

question is is there some
analog of Brownian motion for

the case of a party that is in vacuum and

is experiencing quantum fluctuations
of the electromagnetic field so

let me remind you of the simplest case
of a Brownian motion we would say that

we have a cord in it let's say the center
of this sphere and it has some mass so

mass times acceleration is
equal to the fluctuating force

this is in fully a space or acceleration
became minus Omega square now for

the particle we would also put a D.C.
patient moving the particle that will

cause it friction which is for
the fluid particle.

Particle proportional to
its velocity which are five

fully a transformer if
would get Iomega here.

Now because I am dealing with
a particle that is in vacuum and

special relativity has to be obeyed
there can be no force on a particle

like he's moving with uniform velocity so
the kind of

dissipation that comes about in the
systems one can show is proportional to.

The terror derivative of motion so rather
than having Iomega would have Iomega Q.

as the resource in force this is known
also separately as the Lorentz force.

Now on the right hand side
I have to put a force

that is due to fluctuations Now
suppose that I was dealing with

a charged particle in
a fluctuating electromagnetic field

then the charge particle would experience
a force that will be proportional to

the electric field which is the gradient
let's say of some potential and.

The interesting thing and what we also
assume for the case of Brown and particles

is that even in the quantum case
the electric field being described

by the Lagrangian of electromagnetism
is a quadratic theory and is Galaxy and

distributed so the force would be gaussian
this tree with it if it was charged but

what if I'm dealing with a particle that
is NOT charge is something that is neutral

so a neutral particle the force will
be proportional to polarize ability

times the square of the electric
feast Now the thing that

is important is that whereas the electric
field is Gaussian distributed the square

of the graphs in this review that
object is not Gaussian distributed so

calculating what the effect of this non
go see and distributed force on this.

Dispersion is more complicated and

some of the things that emerges first
of all the depreciation of the particle

does not undergo standard diffusion
it only it's where you and

scrolls logout rhythmically in time and
that's because really the magnetic

field is something that is distributed in
space and so you make some kind of for

the formation that the formation
ultimately will come back on you so

the Markovian character that you have for
ordinary.

Diffusion is not valid in this case but
more interestingly if you look at

the higher moments you find that the way
that the higher moments grow is more

important than the way that the variance
grows and the only way to interpret it

is that rather than getting a Gaussian
dispersion is particularly due to

panto fluctuations will undergo
a kind of dispersion that is poverty.

OK.

So.

In summary.

He started to be de case of the has
a new force of quantum electrodynamics.

We said that it was proposed back
in one nine hundred forty eight and

after fifty years there were sufficiently
high precision experimental operators

to calculate what it was answer
to good extent we can say

that this force has now been
confronted and understood in terms of

experiment and there are some applications
of it that would very much benefit

from weakening were making the force
rather than and I tracked every policy.

That as an example if you like as
a prototype of fluctuation in used force

we can ask whether there are other types
of fluctuation in use forces where rather

than quantum fluctuations Let's say we are
dealing with terrible fog to Asians and

there is indeed a tear mild version of
the Casimir force that was predicted by

Fischer and this year in an experimental
you observed in the binary mixture

of oil of water near criticality and
this force can be

made to be both attractive orderly Parsee
if by playing around the divine and or

conditions then the question is
whether we can do a similar model

of the electromagnetic quantum
causing a force to make it repulsive

either true barring Greece by
introducing these metamaterials or

by play around we did you or
me three of shapes etc and

so level lots of papers proposing this and

what we showed was that there is
some analogue of inshore steal from

that four bit the case of levitation for

Elektra static objects to the case
of Livy Taishan using these.

Casimir forces and as.

Long as your objects are Describe your
board by directory function could

vary as a function of space and
frequency doesn't matter as long as

that is the case then you cannot
have levitation limiting a large

number of theories that had been proposed
based on various our proxy mation.

However by wire leading
the conditions such as by going to out

of equilibrium you can certainly
get examples of this kind of.

Lippy Taishan called your hot
object by the other one because of

radiation pressure but
to do that properly one needs to sort of

think about near field effects and
deal with quantum fluctuations and

there are more fucked relations using this
fluctuation out Q.E.D. of rate of and

the same fluctuation I'll Q.E.D. a writ of
can tell you about some other interesting

effects of non-equal younger motion
is involved we discussed the case of

the flight of a classical particle in
a quantum bat being a kind of dispersive

Levy flight and I mentioned about
the rotating sphere gradually slowing

down because of radiating today
electromagnetic fields so

this work was done at MIT with
a large group of collaborators so

I'm very senior such as Bob Jaffe
my colleague a number of

former and current postdocs
Thorsten images appear we want to.

Know are Graham and.

Students graduate students who have
since graduated and left and I also.

Was wondering how to give you
a justification of looking

at something like this rotating
smearing vacuum and why it is good for.

And I happened to come across
this possible justification.

Thank you for your attention.

It.

Is the.

Classical article yes I'm going on about.

Me You were just wondering if there's
anything interesting to be learned on him.

Also.

Then yeah so I haven't.

Figured out how to do that so

presumably they think is that
somehow the classical part.

Is all these not described by quantum
physics and if I want to put an atom

I have to somehow entangle it already
we did the Cro-Magnon I think feel and

so then maybe the appropriate thing to
do is to start with an initial condition

which is not that and then seeing how that
initial conditions evolves as a function

of time according to the Schroedinger
equation but we haven't done that so

it's a very good question and
it is related or so to divvy that I

have been treated treating everything
else because we certainly know that.

Because of quantum mechanics
the electron rotates along the.

The proton not caring anything about
their choice you are all more gradation

etc Now in the theorems
that I proved I always was

describing the objects through the classic
car dialectic function epsilon of X.

and no make up so at what point that
breaks down and I have to go from

a dielectric description of the material
which is classic cause to a full quantum

description I don't know that's certainly
something that is left to do in this.

Yes.

For.

Just.

One or.

OK So you want to.

Pair.

Let's say I put it particularly in
the battle of quantum fluctuations and

you want to ask what is the difference
between a classical treatment in

which this particle is represented
by a polarizing ability and

using that porous ability to
figure out how much it diffuses

as opposed to the case
where I start to mean.

Some kind of.

Quantum description of
particle that has mass and

is subject to the full
electromagnetic field.

Or OK So then.

OK so you start we debate packet and
you say that because of

the description of quantum mechanics
the big back it would be spread OK so

different that we are seeing is
certainly proportional to see

which you would you wouldn't for
the classical particles so

there would be some or
a shoe off times see an M.

that is in water that can definitely
distinguish those things but

I haven't done the actual calculation but
since our force does depend

on c That is absent in the other case I
know that there would be a distinction.

Or.

Or.

Well this this Zelda which
idea of superior a DNS

indeed comes from the context of black
cores and rotating black horse and.

I understand that people who are looking
at gravitational waves these days

are thinking about whether or

not there are some effects due
to these kinds of radiation so

the radiation also has some kind of
relationship to Hawking radiation and

there's a gravitational wave analogue
of that that one can always of but

certainly this idea that
the boundary conditions of

a rotating object can somehow modify
the phenomenon and have consequences for

radiation is quite general and
potentially will deserve.

To.