In cooperation with students from the University of Louisvile, the Physics
Department and several other multi-disiplenaren associated to modifiy an
edition of Microsoft(r) Outlook(r) as licenced to them by the Microsoft(r)
Corporation.

They were able to find a way to get even older PC's to download,
"SIMULTANEOUSLY AND UPLOAD" text EVEN BINARY files, email, thousands, of
times faster with even older PCS by just ___BELIEVE IT OR NOT--REWRITING
___some of the Microsoft operating code!!!

But as this is the TRUTH, so help me DIE!!!

every man has HIS PRICE! Microsoft found out about the FAST computer when
it detected the VAST number of POSTS everywhere and then STOLE THE PATCH
code and erased the existing copies of it, threatened the STUDENTS and PAID
THEM OFF telling them to keep their mouths shut, hiring them, etc.,
whatever, off course not getting caugth stealing the code, or wiping the
files. AND OF COURSE, we know Microsoft has its friends in government do we
not?

Just look at the posts in the news groups? how could you explain the recent
number of them all?

must be a super duper nin-compooper computer or something like that
would you not agree?

realsmartoday.com
P.O. Box 270029
Louisville Co. 80027


To remove email
http://realsmartoday.com/remove.html

The Internet Connection Wizard helps you connect to one or more e-mail or
news servers. You will need the following information from your Internet
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**** GOOD NEWS !!!

Kirk Gregory Czuhai SAYS !!!

He SAVED HIS NOTES ... AND ...
HE SAYS THAT ...
the superdooper pc computer can
easily be re-constructed from them
Kirk Gregory Czuhai NOW posts
these some of these notes here!
more at:
http://www.altelco.net/~churches/BlueRoses.htm

NOTES:
Kirk Gregory Czuhai

Sunday, August 15, 2004
PHYSICS ((IS)) just !!! SO MUCH PhUn !!!
SINCE SO MANY OF you seem to be somewhat
emamoured by some of the Physics articles
i have written!
the following BLOGS on my part i devote to
"some" physics topics "JUST 4 U!!!"

"I AIM TO PLEASE . . . +++===> "

peace and love,
and,
love and peace,
(kirk) kirk gregory czuhai


posted by Kirk Gregory Czuhai @ 7:39 PM 0 comments

steven jawbones gots it all figured out !!!
Also available at http://math.ucr.edu/home/baez/week207.htmlJuly 25,
2004This Week's Finds in Mathematical Physics - Week 207John Baez I'm
spending the summer in Cambridge, but last week I was in Dublin attending
"GR17", which is short for the 17th International Conference on General
Relativity and Gravitation:1) GR17 homepage,
http://www.dcu.ie/~nolanb/gr17.htmThis is where Stephen Hawking decided to
announce his solution ofthe black hole information loss problem. Hawking is
a media superstar right up there with Einstein and Michael Jackson, so when
reporters heard about this, the ensuing hoopla overshadowed everything else
in the conference. As soon I arrived, one of the organizers complained to me
that they'dhad to spend 4000 pounds on a public relations firm to control
the reporters and other riff-raff who would try to attend Hawking's
talk.Indeed, there seemed to be more than the usual number of crackpots
floating about, though I admit I haven't been to this particular series of
conferences before - perhaps general relativity attracts such people? The
public lecture by Penrose on the last day of the conference may have helped
lure them in. He spoke on "Fashion, Faith and Fantasy in Theoretical
Physics", and people by the door sold copies of his brand new thousand-page
blockbuster:2) Roger Penrose, The Road To Reality: A Complete Guide to the
Physical Universe, Jonathan Cape, 2004.(You may enjoy guessing which popular
theories he classified underthe three categories of fashion, faith and
fantasy.) After his talk, *all* the questions were actually harangues from
people propounding idiosyncratic theories of their own, and the question
period was drawn to an abrupt halt in the middle of one woman's rant about
fractal cosmology. But I bumped into the saddest example when I was having a
chat with some colleagues at a local pub. A fellow with long curly grey
locks and round horn-rimmed glasses sat down beside me. I'd seen him around
the conference, so I said hello. He asked me if I'd like to hear about his
theory; at this point my internal alarm bells started ringing. I told him I
was busy, but said I'd take a look at his manuscript later.It turned out to
describe an idea I'd never even dreamt of before: a heliocentric cosmology
in which the planets move along circular orbits with epicycles a la Ptolemy!
And his evidence comes from a neolithic British tomb called Newgrange. This
tomb may have been aligned to let in the sun on the winter solstice, but
some people doubt this, becauseit seems the alignment would have been
slightly off back in 3200 BC when Newgrange was built. However, it's
slightly off only if you work out the precession of the equinox using
standard astronomy. If you use his theory, it lines up perfectly! Pretty
cute. The only problem is that his paper contains no evidence for this
claim. Instead, it's only a short note sketching the idea, followed by
lengthy attachments containing his correspondence with the Dublin police. In
these, he complained that people were trying to block his patent on a
refrigerator that produces no waste heat. They were constantly flying
airplanes over his house, and playing pranks like boiling water in his
teakettle when he was away, trying to drive him insane. Anyway, on Wednesday
the 21st the whole situation built to a head when Hawking gave his talk in
the grand concert hall of the Royal Dublin Society. As we had been warned,
the PR firm checked our badges at the door. Reporterswith press badges were
also allowed in, so the aisles were soon lined with cameras and recording
equipment. I got there half an hour early to get a good seat, and while I
was waiting, Jenny Hogan from the New Scientist asked if she could interview
me for my reaction afterwards. In short, a thoroughly atypical physics talk!
But you shouldn't imagine the mood as one of breathless anticipation. At
least for the physicists present, a better description would be something
like "skeptical curiosity". None of them seemed to believe that Hawking
could suddenly shed new light on a problem that has been attacked from many
angles for several decades. One reason is that Hawking's best work was done
almost 30 years ago. A string theorist I know said that thanks to work
relating anti-deSitter space and conformal field theory - the so-called
"AdS-CFT" hypothesis - string theorists had become convinced that no
information is lost by black holes. Thus, Hawking had been feeling strong
pressure to fall in line and renounce his previous position, namely that
information *is* lost. A talk announcing this would come as no big surprise.
After a while Kip Thorne, John Preskill, Petros Florides and Hawking'sgrad
student Christophe Galfard came on stage. Then, amid a burst of flashbulbs,
Hawking's wheelchair gradually made its way down the aisle and up a ramp,
attended by a nurse - possibly his wife, I don't know. He had been recently
sick with pneumonia.Once Hawking was on stage, the conference organizer
Petros Florides made an introduction, joking that while physicists believe
no information cantravel faster than light, this seems to have been
contradicted by the speed with which the announcement of Hawking's talk
spread around the globe. Then he recalled the famous bet that Preskill made
with Hawking andThorne. In case you don't know, John Preskill is a leader in
quantumcomputation at Caltech. Kip Thorne is an expert on relativity, also
at Caltech, one of the authors of the famous textbook "Gravitation", and now
playing a key role in the LIGO project to detect gravitational waves. The
bet went like this:Whereas Stephen Hawking and Kip Thorne firmly believe
that information swallowed by a black hole is forever hidden from the
outside universe, and can never be revealed even as the black hole
evaporates and completely disappears,And whereas John Preskill firmly
believes that a mechanism for the information to be released by the
evaporating black hole must and will be found in the correct theory of
quantum gravity,Therefore Preskill offers, and Hawking/Thorne accept, a
wager that:When an initial pure quantum state undergoes gravitational
collapse to form a black hole, the final state at the end of black hole
evaporation will always be a pure quantum state.The loser(s) will reward the
winner(s) with an encyclopedia of the winner's choice, from which
information can be recovered at will.Stephen W. Hawking, Kip S. Thorne, John
P. PreskillPasadena, California, 6 February 1997 It's signed by Thorne and
Preskill, with a thumbprint of Hawking's.After a bit of joking around and an
explanation of how the questionsession would work, Hawking began his talk.
Since it's fairly short and not too easy to summarize, I think I'll just
quote the whole transcript which I believe Sean Carroll got from the New
York Times science reporter Dennis Overbye. I've made a few small
corrections. There were also some slides, but you're not missing a lot by
not seeingthem. The talk was not easy to understand, so unless quantum
gravity isyour specialty you may feel like just skimming it to get the
flavor, andthen reading my attempt at a summary. The talk began with
Hawking's trademark introduction, uttered as usual in his computer-generated
voice:Can you hear me?I want to report that I think I have solved a major
problem intheoretical physics, that has been around since I discovered
thatblack holes radiate thermally, thirty years ago. The question is, is
information lost in black hole evaporation? If it is, the evolution is not
unitary, and pure quantum states, decay into mixed states.I'm grateful to my
graduate student Christophe Galfard for help inpreparing this talk.The black
hole information paradox started in 1967, when WernerIsrael showed that the
Schwarzschild metric, was the only staticvacuum black hole solution. This
was then generalized to the no hairtheorem: the only stationary rotating
black hole solutions of theEinstein-Maxwell equations are the Kerr-Newman
metrics. The no hairtheorem implied that all information about the
collapsing body waslost from the outside region apart from three conserved
quantities:the mass, the angular momentum, and the electric charge.This loss
of information wasn't a problem in the classical theory. Aclassical black
hole would last for ever, and the information could be thought of as
preserved inside it, but just not very accessible. However, the situation
changed when I discovered that quantum effects would cause a black hole to
radiate at a steady rate. At least in the approximation I was using, the
radiation from the black hole would be completely thermal, and would carry
no information. So what would happen to all that information locked inside a
black hole, that evaporated away, and disappeared completely? It seemed the
only way the information could come out would be if the radiation was not
exactly thermal, but had subtle correlations. No one has found a mechanism
to produce correlations, but most physicists believe one must exist. If
information were lost in black holes, pure quantum states would decay into
mixed states, and quantum gravity wouldn't be unitary.I first raised the
question of information loss in '75, and theargument continued for years,
without any resolution eitherway. Finally, it was claimed that the issue was
settled in favour of conservation of information, by AdS/CFT. AdS/CFT is a
conjecturedduality between supergravity in anti-deSitter space and a
conformalfield theory on the boundary of anti-deSitter space at infinity.
Since the conformal field theory is manifestly unitary, the argument is that
supergravity must be information preserving. Any information that falls in a
black hole in anti-deSitter space, must come out again. But it still wasn't
clear how information could get out of a black hole. It is this question I
will address.Black hole formation and evaporation can be thought of as
ascattering process. One sends in particles and radiation frominfinity, and
measures what comes back out to infinity. Allmeasurements are made at
infinity, where fields are weak, and onenever probes the strong field region
in the middle. So one can't be sure a black hole forms, no matter how
certain it might be inclassical theory. I shall show that this possibility
allowsinformation to be preserved and to be returned to infinity.I adopt the
Euclidean approach, the only sane way to do quantumgravity
non-perturbatively. [He grinned at this point.] In this, the time evolution
of an initial state is given by a path integral over all positive definite
metrics that go between two surfaces that are a distance T apart at
infinity. One then Wick rotates the time interval, T, to the Lorentzian.The
path integral is taken over metrics of all possible topologiesthat fit in
between the surfaces. There is the trivial topology: theinitial surface
cross the time interval. Then there are the nontrivial topologies: all the
other possible topologies. The trivial topology can be foliated by a family
of surfaces of constant time. Thepath integral over all metrics with trivial
topology, can be treatedcanonically by time slicing. In other words, the
time evolution(including gravity) will be generated by a Hamiltonian. This
will give a unitary mapping from the initial surface to the final.The
nontrivial topologies cannot be foliated by a family ofsurfaces of constant
time. There will be a fixed point in any timeevolution vector field on a
nontrivial topology. A fixed point in the Euclidean regime corresponds to a
horizon in the Lorentzian. A small change in the state on the initial
surface would propagate as a linear wave on the background of each metric in
the path integral. If the background contained a horizon, the wave would
fall through it,and would decay exponentially at late time outside the
horizon. Forexample, correlation functions decay exponentially in black
holemetrics. This means the path integral over all topologicallynontrivial
metrics will be independent of the state on the initialsurface. It will not
add to the amplitude to go from initial state tofinal that comes from the
path integral over all topologicallytrivial metrics. So the mapping from
initial to final states, given by the path integral over all metrics, will
be unitary. One might question the use in this argument, of the concept of a
quantum state for the gravitational field on an initial or final spacelike
surface. This would be a functional of the geometries of spacelike surfaces,
which is not something that can be measured in weak fields near infinity.
One can measure the weak gravitational fields on a timelike tube around the
system, but the caps at top and bottom, go through the interior of the
system, where the fields may be strong.One way of getting rid of the
difficulties of caps would be to jointhe final surface back to the initial
surface, and integrate over allspatial geometries of the join. If this was
an identification under aLorentzian time interval, T, at infinity, it would
introduce closedtimelike curves. But if the interval at infinity is the
Euclideandistance, beta, the path integral gives the partition function
forgravity at temperature 1/beta.The partition function of a system is the
trace over all states,weighted with e^{-beta H}. One can then integrate beta
alonga contour parallel to the imaginary axis with the factor e^{-beta
E_0}.This projects out the states with energy E_0. In a gravitational
collapse and evaporation, one is interested in states ofdefinite energy,
rather than states of definite temperature.There is an infrared problem with
this idea for asymptotically flatspace. The Euclidean path integral with
period beta is the partitionfunction for space at temperature 1/beta. The
partition function is infinite because the volume of space is infinite. This
infrared problem can be solved by a small negative cosmological constant. It
will not affect the evaporation of a small black hole, but it will change
infinity to anti-deSitter space, and make the thermal partition function
finite.The boundary at infinity is then a torus, S^1 cross S^2. The
trivialtopology, periodically identified anti-deSitter space, fills in the
torus, but so also do nontrivial topologies, the best known of which is
Schwarzschild anti-deSitter. Providing that the temperature is small
compared to the Hawking-Page temperature, the path integral over all
topologically trivial metrics represents self-gravitating radiation in
asymptotically anti-deSitter space. The path integral over all metrics of
Schwarzschild AdS topology represents a black hole and thermal radiation in
asymptotically anti-deSitter.The boundary at infinity has topology S^1 cross
S^2. The simplesttopology that fits inside that boundary is the trivial
topology, S^1 cross D^3, the three-disk. The next simplest topology, and the
first nontrivial topology, is S^2 cross D^2. This is the topology of the
Schwarzschild anti-deSitter metric. There are other possible topologies that
fit inside the boundary, but these two are the important cases:
topologically trivial metrics and the black hole. The black hole is eternal.
It cannot become topologically trivial at late times.In view of this, one
can understand why information is preserved intopologically trivial metrics,
but exponentially decays in topologically non trivial metrics. A final state
of empty spacewithout a black hole would be topologically trivial, and be
foliatedby surfaces of constant time. These would form a 3-cycle modulothe
boundary at infinity. Any global symmetry would lead toconserved global
charges on that 3-cycle. These would preventcorrelation functions from
decaying exponentially in topologicallytrivial metrics. Indeed, one can
regard the unitary Hamiltonianevolution of a topologically trivial metric as
the conservation ofinformation through a 3-cycle.On the other hand, a
nontrivial topology, like a black hole, will not have a final 3-cycle. It
will not therefore have any conservedquantity that will prevent correlation
functions from exponentiallydecaying. One is thus led to the remarkable
result that late timeamplitudes of the path integral over a topologically
non trivialmetric, are independent of the initial state. This was noticed
byMaldacena in the case of asymptotically anti-deSitter in 3d,
andinterpreted as implying that information is lost in the BTZ black
holemetric. Maldacena was able to show that topologically trivial
metricshave correlation functions that do not decay, and have amplitudes
ofthe right order to be compatible with a unitary evolution. Maldacenadid
not realize, however that it follows from a canonical treatmentthat the
evolution of a topologically trivial metric, will be unitary.So in the end,
everyone was right, in a way. Information is lost in topologically
nontrivial metrics, like the eternal black hole. On the other hand,
information is preserved in topologically trivialmetrics. The confusion and
paradox arose because people thoughtclassically, in terms of a single
topology for spacetime. It waseither R^4, or a black hole. But the Feynman
sum over histories allowsit to be both at once. One can not tell which
topology contributed theobservation, any more than one can tell which slit
the electron wentthrough, in the two slits experiment. All that observation
at infinitycan determine is that there is a unitary mapping from initial
statesto final, and that information is not lost.My work with Hartle showed
the radiation could be thought of astunnelling out from inside the black
hole. It was therefore notunreasonable to suppose that it could carry
information out of theblack hole. This explains how a black hole can form,
and then giveout the information about what is inside it, while
remainingtopologically trivial. There is no baby universe branching off, as
I once thought. The information remains firmly in our universe. I'm sorry to
disappoint science fiction fans, but if information ispreserved, there is no
possibility of using black holes to travel toother universes. If you jump
into a black hole, your mass-energy willbe returned to our universe, but in
a mangled form, which contains theinformation about what you were like, but
in an unrecognisable state.There is a problem describing what happens,
because strictly speakingthe only observables in quantum gravity are the
values of the fieldat infinity. One cannot define the field at some point in
the middle,because there is quantum uncertainty in where the measurement
isdone. However, in cases in which there are a large number, N, of light
matter fields, coupled to gravity, one can neglect the gravitational
fluctuations, because they are only one among N quantum loops. One can then
do the path integral over all matter fields, in a given metric, to obtain
the effective action, which will be a functional of the metric.One can add
the classical Einstein-Hilbert action of the metric tothis quantum effective
action of the matter fields. If one integratedthis combined action over all
metrics, one would obtain the fullquantum theory. However, the semiclassical
approximation is torepresent the integral over metrics by its saddle point.
This willobey the Einstein equations, where the source is the expectation
valueof the energy momentum tensor, of the matter fields in their
vacuumstate.The only way to calculate the effective action of the matter
fields,used to be perturbation theory. This is not likely to work in the
caseof gravitational collapse. However, fortunately we now have
anon-perturbative method in AdS/CFT. The Maldacena conjecture saysthat the
effective action of a CFT on a background metric is equal tothe supergravity
effective action of anti-deSitter space with thatbackground metric at
infinity. In the large N limit, the supergravityeffective action is just the
classical action. Thus the calculationof the quantum effective action of the
matter fields, is equivalent tosolving the classical Einstein equations.The
action of an anti-deSitter-like space with a boundary atinfinity would be
infinite, so one has to regularize. One introduces subtractions that depend
only on the metric of the boundary.The first counter-term is proportional to
the volume of the boundary. The second counter-term is proportional to the
Einstein-Hilbert actionof the boundary. There is a third counter-term, but
it is not covariantly defined. One now adds the Einstein-Hilbert action of
the boundary and looks for a saddle point of the total action. This will
involve solving the coupled four- and five-dimensional Einstein equations.
It will probably have to be done numerically.In this talk, I have argued
that quantum gravity is unitary, andinformation is preserved in black hole
formation and evaporation. I assume the evolution is given by a Euclidean
path integral overmetrics of all topologies. The integral over topologically
trivialmetrics can be done by dividing the time interval into thin slicesand
using a linear interpolation to the metric in each slice. Theintegral over
each slice will be unitary, and so the whole pathintegral will be unitary.On
the other hand, the path integral over topologically nontrivialmetrics, will
lose information, and will be asymptotically independentof its initial
conditions. Thus the total path integral will beunitary, and quantum
mechanics is safe.It is great to solve a problem that has been troubling me
for nearlythirty years, even though the answer is less exciting than
thealternative I suggested. This result is not all negative however,because
it indicates that a black hole evaporates, while remainingtopologically
trivial. However, the large N solution is likely to be a black hole that
shrinks to zero. This is what I suggested in 1975.In 1997, Kip Thorne and I
bet John Preskill that information waslost in black holes. The loser or
losers of the bet are to providethe winner or winners with an encyclopaedia
of their own choice, fromwhich information can be recovered with ease. I'm
now ready to concedethe bet, but Kip Thorne isn't convinced just yet. I will
give JohnPreskill the encyclopaedia he has requested. John is all-American,
sonaturally he wants an encyclopaedia of baseball. I had great difficulty in
finding one over here, so I offered him an encyclopaedia of cricket, as an
alternative, but John wouldn't be persuaded of the superiority of cricket.
Fortunately, my assistant, Andrew Dunn, persuaded the publishers
Sportclassic Books to fly a copy of "Total Baseball: The Ultimate Baseball
Encyclopedia" to Dublin. I will give John the encyclopaedia now. If Kip
agrees to concede the bet later, hecan pay me back.After this, Kip Thorne
ran a question and answer period, saying thathe would alternate between
questions from conference participants,which Hawking's grad student would
answer, and questions from the press, which Hawking would answer - after
Thorne checked Hawking's facial expressions to see whether he felt they were
worth answering. First, a correspondent from the BBC asked Stephen Hawking
what the significance of this result was for "life, the universe and
everything". (Here I'm using John Preskill's humorous paraphrase.) Hawking
agreedto answer this, and while he began laboriously composing a reply using
the computer system on his wheelchair, his grad student Christophe Galfard
fielded three questions from experts: Bill Unruh, Gary Horowitz and Robb
Mann. I didn't find the replies terribly illuminating, except that when
asked if information would be lost if we kept feeding the black hole matter
to keep it from evaporating away, Galfard said "yes". Everyoneafterwards
commented on what a tough job it would be for a student to field questions
in front of about 800 physicists and the international press. At this point
Kip Thorne checked to see if Hawking was done composinghis reply. He was
not. To fill time, Thorne explained why he hadn'tyet conceded the bet,
saying that while the talk seemed convincing to him, he still wanted to see
the details. He explained to the reportersa bit about how science was done:
we don't just listen to Hawking andtake his word for everything, we have to
go off and calculate things ourselves. He told a nice story about how when
Hawking first showedthat black holes radiate, everyone with their own
approach to quantumfield theory on curved spacetime needed to redo this
calculation theirown way to be convinced - with Yakov Zeldovich, who'd
gotten the gamestarted by showing that energy could be extracted from
*rotating* blackholes in the form of radiation, being one of the very last
to agree!Preskill chimed in by saying "I'll be honest - I didn't understand
thetalk", adding that would need to see more details. After a bit more of
this sort of thing, Hawking was ready to answerthe BBC reporter's question.
His answer was surprisingly short, and itwent something like this (I can't
find an exact quote): "This resultshows that everything in the universe is
governed by the laws of physics." A suitably grandiose answer for a
grandiose question!One can imagine much better explanations of unitarity,
but not veryquick ones.At this point Kip Thorne solicited more questions
from the press butsaid they should confine themselves to questions with
yes-or-no answers.Jenny Hogan got off the first one, asking what Hawking
would do nowthat he's solved this problem. Kip Thorne pointed out that this
wasnot a yes-or-no question, but in the midst of the ensuing
conversationHawking shot off an unexpectedly rapid reply: "I don't know."
Everyonelaughed, and at this point the public question period was called to
a close,though reporters were allowed to stay and pester Hawking some
more.At the time Hawking's talk seemed very cryptic to me, but in the
processof editing the above transcript it's become a lot clearer, so I'll
tryto give a quick explanation. I should start by saying that the jargon
used in this talk, while doubtless obscure to most people, is actually quite
standard and not very difficult to anyone who has spent some time studying
the Euclidean path integral approach to quantum gravity. The problem is not
the jargon so much as the lack of detail, which requires some imagination to
fill in. When I first heard the talk, this lack of detail had mecompletely
stumped. But now it makes a little more sense....He's studying the process
of creating a black hole and letting itevaporate away. He's imagining
studying this in the usual styleof particle physics, as a "scattering
experiment", where we throw ina bunch of particles and see what comes out.
Here we throw in a bunchof particles, let them form a black hole, let the
black hole evaporateaway, and examine the particles (typically photons for
the most part) that shoot out. The rules of the game in a "scattering
experiment" are that we can only talk about what's going on "at infinity",
meaning very far from where the black hole forms - or more precisely, where
it mayor may not form! The advantage of this is that physics at infinity can
be described without the full machinery of quantum gravity: we don't have to
worry about quantum fluctuations of the geometry of spacetime messing up our
ability to say where things are. The disadvantage is that we can't actually
say for sure whether or not a black hole formed. Atleast this *seems* like a
"disadvantage" at first - but a better term for it might be a "subtlety",
since it's crucial for resolving the puzzle:Black hole formation and
evaporation can be thought of as ascattering process. One sends in particles
and radiation frominfinity, and measures what comes back out to infinity.
Allmeasurements are made at infinity, where fields are weak, and onenever
probes the strong field region in the middle. So one can't be sure a black
hole forms, no matter how certain it might be inclassical theory. I shall
show that this possibility allowsinformation to be preserved and to be
returned to infinity.Now, the way Hawking likes to calculate things in this
sort of problem is using a "Euclidean path integral". This is a
rathercontroversial approach - hence his grin when he said it's the "only
sane way" to do these calculation - but let's not worry aboutthat. Suffice
it to say that we replace the time variable "T"in all our calculations by
"iT", do a bunch of calculations, and then replace "iT" by "T" again at the
end. This trick is called"Wick rotation". In the middle of this process, we
hope all our formulas involving the geometry of 4d *spacetime* have
magically become formulas involving the geometry of 4d *space*. The answers
to physical questions are then expressed as integrals over all geometries of
4d space that satisfy some conditions depending on the problem we're
studying. This integral over geometries alsoincludes a sum over topologies.
That's what Hawking means by this:I adopt the Euclidean approach, the only
sane way to do quantumgravity non-perturbatively. In this, the time
evolution of an initial state is given by a path integral over all positive
definite metrics that go between two surfaces that are a distance T apart at
infinity. One then Wick rotates the time interval, T, to the Lorentzian. The
path integral is taken over metrics of all possible topologies that fit in
between the surfaces. Unfortunately, nobody knows how to define these
integrals. However,physicists like Hawking are usually content to compute
them in a"semiclassical approximation". This means integrating not over
allgeometries, but only those that are close to some solution of the
classical equations of general relativity. We can then do a clever
approximation to get a closed-form answer.(Nota bene: here I'm talking about
the equations of general relativityon 4d *space*, not 4d spacetime. That's
because we're in the middleof this Wick rotation trick.)Actually, I'm
oversimplifying a bit. We don't get "the answer" toour physics question this
way: we get one answer for each solution of the equations of general
relativity that we deem relevant to the problem at hand. To finish the job,
we should add up all these partialanswers to get the total answer. But in
practice this last step is always too hard: there are too many topologies,
and too many classicalsolutions, to keep track of them all.So what do we do?
We just add up a few of the answers, cross our fingers, and hope for the
best! If this procedure offends you, go do something easy like math.In the
problem at hand here, Hawking focuses on two classical solutions,or more
precisely two classes of them. One describes a spacetime with no black hole,
the other describes a spacetime with a black hole which lastsforever. Each
one gives a contribution to the semiclassical approximation of the integral
over all geometries. To get answers to physical questions, he needs to sum
over *both*. In principle he should sum over infinitely many others, too,
but nobody knows how, so he's probably hoping the crux of the problem can be
understood by considering just these two. He says that if you just do the
integral over geometries near theclassical solution where there's no black
hole, you'll find - unsurprisingly - that no information is lost as time
passes.He also says that if you do the integral over geometries near
theclassical solution where there is a black hole, you'll
find -surprisingly - that the answer is *zero* for a lot of questions you
can measure the answers to far from the black hole. In physics jargon, this
is because a bunch of "correlation functions decay exponentially". So, when
you add up both answers to see if information is lost in thereal problem,
where you can't be sure if there's a black hole or not,you get the same
answer as if there were no black hole! So in the end, everyone was right, in
a way. Information is lost in topologically nontrivial metrics, like the
eternal black hole. On the other hand, information is preserved in
topologically trivialmetrics. The confusion and paradox arose because people
thoughtclassically, in terms of a single topology for spacetime. It
waseither R^4, or a black hole. But the Feynman sum over histories allowsit
to be both at once. One can not tell which topology contributed
theobservation, any more than one can tell which slit the electron
wentthrough, in the two slits experiment. All that observation at
infinitycan determine is that there is a unitary mapping from initial
statesto final, and that information is not lost.The mysterious part is why
the geometries near the classical solution where there's a black hole don't
contribute at all to information loss, even though they do contribute to
other important things, like theHawking radiation. Here I'd need to see an
actual calculation. Hawkinggives a nice hand-wavy topological argument, but
that's not enough forme. Since this issue is long enough already and I want
to get it out soon,I won't talk about other things that happened at this
conference - norwill I talk about the conference on n-categories earlier
this summer!I just want to say a few elementary things about the topology
lurking in Hawking's talk... since some mathematicians may enjoy it. As he
points out, the answers to a bunch of questions diverge unless we put our
black hole in a box of finite size. A convenient wayto do this is to
introduce a small negative cosmological constant,which changes our default
picture of spacetime from Minkowski spacetime,which is topologically R^4, to
anti-deSitter spacetime, which is topologically R x D^3 after we add the
"boundary at infinity". Here R is time and the 3-disk D^3 is space. This is
a Lorentzian manifold with boundary, but when we do Wick rotation we get a
Riemannianmanifold with boundary having the same topology. However, when we
are doing Euclidean path integrals at nonzero temperature, we should replace
the time line R here by a circle whose radius is the reciprocal of that
temperature. (Take my word for it!) So now our Riemannian manifold with
boundary is S^1 x D^3. This is what Hawking uses to handle the geometries
without a blackhole. The boundary of this manifold is S^1 x S^2. But there's
another obvious manifold with this boundary, namely D^2 x S^2. And this
corresponds to the geometries with a black hole! This is cutebecause we see
it all the time in surgery theory. In fact I commentedon Hawking's use of
this idea a long time ago, in "week67". In his talk, Hawking points out that
S^1 x D^3 has a nontrivial 3-cycle in it if we use relative cohomology and
work relative to the boundaryS^1 x S^2. But, D^2 x S^2 does not. When
spacetime is n-dimensional, conservation laws usually come from integrating
closed (n-1)-forms over cycles that correspond to "space", so we get
interesting conservation laws when there are nontrivial (n-1)-cycles. Here
Hawking is using this toargue for conservation of information when there's
no black hole - namelyfor S^1 x D^3 - but not when there is, namely for D^2
x S^2. All this is fine and dandy; the hard part is to see why the case when
there *is* a black hole doesn't screw things up! This is where his allusions
to "exponentially decaying correlation functions come in" - and this is
where I'd like to see more details. I guess a good place to start
isMaldacena's papers on the black hole in 3d spacetime - the so-called
Banados-Teitelboim-Zanelli or "BTZ" black hole. This is a baby version of
the problem, one dimension down from the real thing, where everything should
get much simpler. For the original BTZ paper, try:3) Maximo Banados, Marc
Henneaux, Claudio Teitelboim, and Jorge Zanelli,Geometry of the 2+1 black
hole, available as gr-qc/9302012.Maldacena's papers can also be found on the
physics arXiv, but I'mnot sure which one Hawking is referring to, so I'll
wait until someonetells me before adding a link to that one. Sometime I will
also add linksto a bunch of photos taken at this conference - including
photos of the plaque under the bridge where Hamilton wrote his defining
relations for the
quaternions!----------------------------------------------------------------
-------Previous issues of "This Week's Finds" and other expository articles
onmathematics and physics, as well as some of my research papers, can
beobtained athttp://math.ucr.edu/home/baez/For a table of contents of all
the issues of This Week's Finds, tryhttp://math.ucr.edu/home/baez/twf.htmlA
simple jumping-off point to the old issues is available
athttp://math.ucr.edu/home/baez/twfshort.htmlIf you just want the latest
issue, go tohttp://math.ucr.edu/home/baez/this.week.html


posted by Kirk Gregory Czuhai @ 7:33 PM 0 comments

Saturday, August 14, 2004
dumb polack?
Son comes to his father.
"Dad," he asks, "do you know where Poland is?"
"I don't know son, but it couldn't be far away,
'cos we have that dumb Polack at work, and he once said
that it only takes him 15 minutes to get to work."
--------------
How can one tell a good Thai restaurant?
Thai people eat there.
How can one tell a good French restaurant?
French people eat there.
How can one tell a good Japanese restaurant?
Japanese people eat there.
How can one tell a really bad Polish restaurant?
Americans eat there.
2nd punchline:
Is it really bad because they eat there,
or do they eat there becuse it's really bad?
--------------
enjoy...
peace and love,
(kirk) kirk gregory czuhai


posted by Kirk Gregory Czuhai @ 9:14 PM 0 comments

physics PHUN 4u !!!
------------------------- A theoretical physics
FAQ -------------------------
http://www.mat.univie.ac.at/~neum/physics-faq.txt Here are answers to some
frequently asked questions from theoretical physics. They were collected
from my answers to postings to the newsgroup sci.physics.research. Of course
they refer only to a tiny part of theoretical physics, and they are only as
good as my understanding of the matter. This doesn't mean that they are
poor... But if you have suggestions for improvements, please write me at
Arnold.Neumaier@univie.ac.at If you have questions, please post them to the
newsgroup sci.physics.research (http://www.lns.cornell.edu/spr)! Happy
Reading! Arnold Neumaier University of Vienna
http://www.mat.univie.ac.at/~neum/ Abbreviations: QM = quantum mechanics.
QFT = quantum field theory. QED = quantum electrodynamics. s.p.r =
sci.physics.research (newsgroup). Strings like quant-ph/0303047 refer to
electronic documents in the e-Print archive (see
http://xxx.lanl.gov/). ----------------- Table of Contents -----------------
(The labels may change with time as answers to further questions will be
added. So, to quote part of the FAQ, refer to the title of a section and not
to its label.) 1a. Are electrons pointlike/structureless? 1b. What are
'bare' and 'dressed' particles? 1c. How meaningful are single Feynman
diagrams? 1d. How real are 'virtual particles'? 1e. What is the meaning of
'on-shell' and 'off-shell'? 1f. Virtual particles and Coulomb interaction
1g. Are virtual particles and decaying particles (resonances) the same? 1h.
Can particles go backward in time? 1i. What about particles faster than
light (tachyons)? 2a. Summing divergent series 2b. Nonperturbative
computations in QFT 2c. Functional integrals, Wightman functions, and
rigorous QFT 2d. Is there a rigorous interacting QFT in 4 dimensions? 2e. Is
QED consistent? 2f. Bound states in relativistic QFT 2g. Why bother about
rigor in physics? 2h. Why normal ordering? 3a. Is there a multiparticle
relativistic quantum mechanics? 3b. Localization and position operators 3c.
Representations of the Poincare group, spin and gauge invariance 4a. A
concise formulation of the measurement problem of QM 4b. The double slit
experiment 4c. The Stern-Gerlach experiment 4d. The minimal interpretation
4e. The preferred basis problem 4f. Does decoherence solve the measurement
problem? 4g. Which interpretation of quantum mechanics is most consistent?
4h. What about relativistic measurement theory? 5a. Random numbers in
probability theory 5b. How meaningful are probabilities of single events?
5c. How do probabilities apply in practice? 5d. Priors and entropy in
probability theory 6a What are bras and kets? 6b. What is the meaning of the
entries of a density matrix? 7a. What is the tetrad formalism? 7b. Energy in
general relativity 7c. Difficulties in quantizing gravity 7d. Is quantum
mechanics compatible with general relativity? 7e. Why do gravitons have spin
2? 8a. Theoretical challenges close to experimental data 98a. Background
needed for theoretical physics 99a.
Acknowledgments -------------------------------------- Are electrons
pointlike/structureless? -------------------------------------- Both
electrons and neutrinos are considered to be pointlike as bare particles,
because of the way they appear in the standard model. But physical,
relativistic particles are not pointlike. An intuitive argument for this is
the fact that their localization to a region siognificantly smaller than the
de Broglie wavelength would need energies larger than that needed to create
particle-antiparticle pairs, which changes the nature of the system. (See
also this FAQ about localization, and Foldy's papers quoted there.) On a
more formal, quantitative level, the physical, dressed particles have
nontrivial form factors, due to the renormalization necessary to give finite
results in QFT. Nontrivial form factors give rise leading to a positive
charge radius. In his book S. Weinberg, The quantum theory of fields, Vol.
I, Cambridge University Press, 1995, Weinberg defines and explicitly
computes in (11.3.33) the 'charge radius' of a physical electron. But his
formula is not fully satisfying since it is not fully renormalized (infrared
divergence: the expression contains a ficticious photon mass, and diverges
if this goes to zero). (28) in hep-ph/0002158 = Physics Reports 342, 63-26
(2001) handles this using a binding energy dependent cutoff, which makes the
electron charge radius depend on its surrounding. The paper L.L. Foldy,
Neutron-electron interaction, Rev. Mod. Phys. 30, 471-481 (1958). discusses
the extendedness of the electron in a phenomenological way. On the numerical
side, I only found values for the charge radius of the neutrinos, computed
from the standard model to 1 loop order. The values are about 4-6 10^-14 cm
for the three neutrino species. See (7.12) in Phys. Rev. D 62, 113012 (2000)
http://adsabs.harvard.edu/cgi-bin/np...hDT.......130L gives in
an abstract of a 1982 thesis of Anzhi Lai an electron charge radius of ~
10^{-16} cm (But I haven't seen the thesis.) The "form" of an elementary
particle is described by its form factor, which is a well-defined physical
function (though at present computable only in perturbation theory)
describing how the (spin 0, 1/2, or 1) particle's response to an external
classical electromagnetic field deviates from the Klein-Gordon, Dirac, or
Maxwell equations, respectively. In Foldy's paper, the form factors are
encoded in the infinite sum in (16). The sum is usually considered in the
momentum domain; then one simply gets two k-dependent form factors, where k
represents the 4-momentum transferred in the interaction. These form factors
can be calculated in a good approximation perturbatively from QFT, see for
example Peskin and Schroeder's book. An extensive discussion of form factors
of Dirac particles and their relation to the radial density function is in
D. R. Yennie, M. M. Levy and D. G. Ravenhall, Electromagnetic Structure of
Nucleons, Rev. Mod. Phys. 29, 144-157 (1957). and R. G. Sachs High-Energy
Behavior of Nucleon Electromagnetic Form Factors Phys. Rev. 126, 2256-2260
(1962) For proton and neutron form factors, see hep-ph/0204239 and
hep-ph/0303054 ---------------------------------------- What are 'bare' and
'dressed' particles? ---------------------------------------- A bare
electron is the formal entity discussed in textbooks when they do
perturbative quantum electrodynamics. The intuitive picture generally given
is that a bare electron is surrounded by a cloud of virtual photons and
virtual electron-positron pairs to make up a physical, 'dressed' electron.
Only the latter is real and observable. The former is a formal caricature of
the latter, with paradoxical properties (infinite mass, etc.). On a more
substantial level, the observable electrons are produced from the bare
electrons by a process called renormalization, which modifies the
propagators by self-energy terms and the currents by form factors. As the
name says, the latter define the 'form' of a particle. (In the above
picture, it would correspond to the shape of the virtual cloud, though it is
better to avoid giving the virtual particles too much of meaning.) The
dressed object is the renormalized, physical object, described
perturbatively as the bare object 'clothed' by the cloud of virtual
particles. The dressed interaction is the 'screened' physical interaction
between these dress objects. To draw an analogy in nonrelativistic QM think
of nuclei as bare atoms, electrons as virtual particles, atoms as dressed
nuclei and the residual interaction between atoms, computed in the
Born-Oppenheimer approximation, as the dressed interaction. Thus, for Argon
atoms, the dressed interaction is something close to a Lennard-Jones
potential, while the bare interaction is Coulomb repulsion. This is the
situation physicists had in mind when they invented the notions of bare and
dressed particles. Of course, it is only an analogy, and should not be taken
very seriously. It just explains the intuition about the terminology used.
The electrons in QM are real, physical electrons that can be isolated. The
reason is that they are good eigenstates of the Hamiltonian. On the other
hand, virtual particles don't have this nice attribute since the
relativistic Hamiltonian H from field theory contains creation and
annihilation operators which mess things up. The bare particles correspond
to 1-particle states in the Hilbert space (though that is not quite true
since there is no good Hilbert space picture in conventional interacting
QFT). Multiplying them with H introduces terms with other particle numbers,
hence a bare particle can never be an eigenstate of H, and thus never be
observable in the way a nonrelativistic particle is. The eigenstates of the
relativistic Hamiltonian are, instead, complicated multibody states
consisting of a superposition of states with any number of particles and
antiparticles, just subject to the restriction that the total quantum
numbers come out right. These are the dressed
particles. ------------------------------------------- How meaningful are
single Feynman diagrams? ------------------------------------------- The
standard model is a theory defined in terms of a Lagrangian. To get
computable output, Feynman graph techniques are used. But individual Feynman
graphs are meaningless (often infinite); only the sum of all terms of a
given order can be given - after a process called renormalization - a
well-defined (finite) meaning. This is well-known; so no-one treats the
Feynman graphs as real. What is taken as real is the final outcome of the
calculations, which can be compared with
measurements. --------------------------------- How real are 'virtual
particles'? --------------------------------- All language is only an
approximation to reality, which simply is. But to do science we need to
classify the aspects of reality that appear to have more permanence, and
consider them as real. Nevertheless, all concepts, including 'real' have a
fuzziness about them, unless they are phrased in terms of rigorous
mathematical models (in which case they don't apply to reality itself but
only to a model of reality). In the informal way I use the notion, 'real' in
theoretical physics means a concept or object that - is independent of the
computational scheme used to extract information from a theory, - has a
reasonably well-defined and consistent formal basis - does not give rise to
misleading intuition. This does not give a clear definition of real, of
course. But it makes charge distributions and inputs and outputs of
(theoretical models of) scattering experiments something real, while making
bare particles and virtual particles artifacts of perturbation theory.
'Real' real particles are slightly different from 'mathematical' real
particles. Note that whenever we observe a system we make a number of
idealizations that serve to identify the objects in reality with the
mathematical concepts we are using to describe them. Then we calculate
something, and at the end we retranslate it into reality. If our initial
initialization was good enough and our theory is good enough, the final
result will match reality well. Modern QED and other field theories are
based on the theory developed for modeling scattering events. Now scattering
events take a very short time compared to the lifetime of the objects
involved before and after the event. Therefore, we represent a prepared beam
of particles hitting a target as a single particle hitting another single
particle, and whenever this in fact happens, we observe end products, e.g.
in a wire chamber. Strictly speaking (i.e., in a fuller model of reality),
we'd have to use a multiparticle (statistical mechanics) setting, but this
is never done since it does not give better information and the added
complications are formidable. As long as we prepare the particles long
(compared to the scattering time) before they scatter and observe them long
enough afterwards, they behave essentially as in and out states,
respectively. (They are not quite free, because of the electromagnetic
self-field they generate, this gives rise to the infrared problem in QED and
can be corrected by using coherent states.) The preparation and detection of
the particles is outside this model, since it would produce only minute
corrections to the scattering event. But to treat it would require to
increase the system to include source and detector, which makes the problem
completely different. Therefore at the level appropriate to a scattering
event, the 'real' real particles are modeled by 'mathematical' in/out
states, which therefore are also called 'real'. On the other hand,
'mathematical' virtual particles have nothing to do with observations, hence
have no counterpart in reality; therefore they are called 'virtual'. The
figurative virtual objects in QFT are there only because of the well-known
limitations of the foundations of QFT. In a nonperturbative setting they
wouldn't occur at all. This can be seen by comparing with QM. One could also
do nonrelativistic QM with virtual objects but no one does so (except
sometimes in motivations for QFT), because it does not add value to a
well-understood theory. Virtual particles are an artifice of perturbation
theory that give an intuitive (but if taken too far, misleading)
interpretation for Feynman diagrams. More precisely, a virtual photon, say,
is an internal photon line in one of the Feynman diagrams. But there is
nothing real associated with it. Detectable photons are always real,
'dressed' photons. Virtual particles, and the Feynman diagrams they appear
in, are just a visual tool of keeping track of the different terms in a
formal expansion of scattering amplitudes into multi-dimensional integrals
involving multiple Green's functions - the virtual particle momenta
represent the integration variables. They have no meaning at all outside
these integrals. Thus they get out of mathematical existence once one
changes the formula for computing a scattering amplitude. Therefore virtual
particles are somehow analogous to virtual integers k obtained by computing
log(1-x) = sum_k x^k/k by expansion into a Taylor series. Since we can
compute the logarithm in many other ways, it is ridiculous to attach to k
any intrinsic meaning. But ... ... in QFT, we have no good ways to compute
scattering amplitudes without at least some form of expansion (unless we use
the lowest order of some approximation method), which makes virtual
particles look a little more real. But the analogy to the Taylor series
shows that it's best not to look at them that way. (For a very informal view
of QED in terms of clouds of virtual particles see
http://groups.google.com/groups?selm...40univie.ac.at and
the later mails in this thread.) A sign of the irreality of virtual
particles is the fact that when you do partial resummations of diagrams,
many of the virtual particles disappear. A fully nonperturbative theory
would sum everything, and no virtual particles would be present anymore.
Thus virtual particles are entirely a consequence of looking at QFT in a
perturbative way rather than nonperturbatively. In the standard covariant
Feynman approach, energy (cp_0) and momentum (\p; the backslash indicates
'boldface') is conserved, and virtual particles are typically off-shell
(i.e., they do not satisfy the equation p^2 = p_0^2 - \p^2 = m^2 for
physical particles). To see this, try to model a vertex in which an electron
(mass m_e) absorbs a photon (mass 0). One cannot keep the incoming electron
and photon and the outgoing photon on-shell (satisfying p^2 = m^2) without
violating the energy-momentum balance. However, when working in light front
quantization, one keeps all particles on-shell, and instead has energy and
momentum nonconservation (removed formally by adding an additional
'spurion'). The effect of this is that the virtual particle structure of the
theory is changed completely: For example, the physical vacuum and the bare
vacuum now agree, while in the standard approach, the vacuum looks like a
highly complicated medium made up from infinitely many bare particles....
But phyiscal particles must still be dressed, though less heavily than in
the traditional Feynman approach. Clearly concepts such as virtual particles
that depend so much on the method of quantization cannot be regarded as
being real. See also earlier discussions on s.p.r. such as
http://www.lns.cornell.edu/spr/2003-06/msg0051674.html also
http://www.lns.cornell.edu/spr/1999-02/msg0014762.html and followups; maybe
http://www.lns.cornell.edu/spr/2003-05/msg0051023.html is also of interest.
[For a longwinded alternative view of virtual particles that I do _not_
share but rather find misleading, see
http://www.desy.de/user/projects/Phy...articles.html] ---
----------------------------------------------- What is the meaning of
'on-shell' and
'off-shell'? -------------------------------------------------- This applies
only to relativistic particles. A particle of mass m is on-shell if its
momentum p satisfies p^2 (= p_0^2-p_1^2-p_2^2-p_3^2) = m^2, and off-shell
otherwise. The 'mass shell' is the manifold of momenta p with p^2=m^2.
Observable (i.e., physical) particles are asymptotic states (scattering
states) described (modulo unresolved mathematical difficulties) by free
fields based on the dispersion relation p^2=m^2, and hence are necessarily
on-shell. Off-shell particles only arise in intermediate perturbative
calculations; they are necessarily 'virtual'. The situation is muddled by
the fact that one has to distinguish (formal) bare mass and (physical)
dressed mass; the above is valid only for the dressed mass. Moreover, the
mass shell loses its meaning in external fields, where, instead, a so-called
'gap equation' appears. ----------------------------------------- Virtual
particles and Coulomb interaction -----------------------------------------
Virtual objects have strange properties. For example, the Coulomb
interaction between two electrons is mediated by virtual photons faster than
the speed of light, with imaginary masses. (This is often made palatable by
invoking a time-energy uncertaintly relation, which would allow particles to
go off-shell. But there is no time operator in QFT, so the analogy to
Heisenberg's uncertainty relation for position and momentum is highly
dubious.) Strictly speaking, the Coulomb interaction is simply the Fourier
transform of the photon propagator 1/q^2, followed by a nonrelativistic
approximation. It has nothing at all to do with virtual particle
exchanges --- except if you do perturbation theory. But then there is no
surprise that it must influence already the tree level. By a hand waving
argument (equate the Born approximations) this gives the nonrelativistic
correspondence. But to get the Coulomb interaction as part of the
Schroedinger equation, you need to sum all ladder diagrams with
0,1,2,3,...,n,... exchanged photons arranged in form of a ladder. Then one
needs to approximate the resulting Bethe-Salpeter equation. These are
nonperturbative techniques. (The computations are still done at few loops
only, which means that questions of convergence never enter.) Virtual
photons mediating the Coulomb repulsion between electrons have spacelike
momenta and hence would proceed faster than light if there were any reality
to them. But there cannot be; you'd need infinitely many of them, and
infinitely many virtual electron-positron pairs (and then superpositions of
any numbers of these) to match exactly a real, dressed object or
interaction. ---------------------------------------------------------------
---- Are virtual particles and decaying particles (resonances) the
same? ------------------------------------------------------------------- A
very sharp resonance has a long lifetime relative to a scattering event,
hence behaves like a particle in scattering. It is regarded as a real object
if it lives long enough that its trace in a wire chamber is detectable, or
if its decay products are detectable at places significantly different from
the place where it was created. On the other hand, a very broad resonance
has a very short lifetime and cannot be differentiated well from the
scattering event producing it; so the idealization defining the scattering
event is no longer valid, and one would not regard the resonance as a
particle. Of course, there is an intermediate grey regime where different
people apply different judgment. This can be seen, e.g., in discussions
concerning the tables of the Particle Data Group. The only difference
between a short-living particle and a stable particle is the fact that the
stable particle has a real rest mass, while the mass m of the resonance has
a small imaginary part. Note that states with complex masses can be handled
well in a rigged Hilbert space (= Gelfand triple) formulation of quantum
mechanics. Resonances appear as so-called Siegert (or Gamov) states. A good
reference on resonances (not well covered in textbooks) is V.I. Kukulin et
al., Theory of Resonances, Kluwer, Dordrecht 1989. For rigged Hilbert spaces
(treated in Appendix A of Kukulin), see also quant-ph/9805063 and for its
functional analysis ramifications, K. Maurin, General Eigenfunction
Expansions and Unitary Representations of Topological Groups, PWN Polish
Sci. Publ., Warsaw 1968. But a very short-living particle is usually not the
same as a virtual particle. Instead, it is a complicated, nearly bound state
of other particles. On the other hand, virtual particles are essentally
always elementary. (There are exceptions when deriving Bethe-Salpeter
equations and the like for the approximate calculations of bound states and
resonances, where one creates an effective theory in which the latter are
treated as elementary.) The difference can also be seen in the mathematical
representation. In an effective theory where the resonance (e.g., the
neutron or a meson) is regarded as an elementary object, the resonance again
appears in in/out states as a real particle, with complex on shell momentum
satisfying p^2=m^2, but in internal Feynman diagrams as a virtual particle
with real mass, almost always off-shell, i.e., violating this equation.
However, there are some unstable elementary particles like the weak gauge
bosons. Usually, you observe a 4-fermion interaction and the gauge bosons
are virtual. But at high energy = very short scales, you can in principle
observe the gauge bosons and make them real. Now I don't know if they were
observed as particle tracks or only as resonances (i.e. indirect evidence
from 4-fermion cross sections). And I don't know how people actually model
this situation. Maybe there are experts who can provide further details on
this. In any case, from a mathematical point of view, you must choose the
framework. Either one works in a Hilbert space, then masses are real and
there are no unstable particles (since these 'are' poles on the so-called
'unphysical' sheet); in this case, there are no asymptotic gauge bosons and
all are therefore virtual. Or one works in a rigged Hilbert space and deform
the inner product; this makes part of the 'unphysical' sheet visible; then
the gauge bosons have complex masses and there exist unstable particles
corresponding to in/out gauge bosons which are real. The modeling framework
therefore decides which language is
appropriate. ---------------------------------- Can particles go backward in
time? ---------------------------------- In the old relativistic QM (for
example in Volume 1 of Bjorken and Drell) antiparticles are viewed as
particles traveling backward in time. This is based on a consideration of
the solutions of the Dirac equation and the idea of a filled sea of
negative-energy solutions in which antiparticles appear as holes (though
this picture only works for fermions since it requires an exclusion
principle). One can go some way with this view, but more sophisticated stuff
requires the QFT picture (as in Volume 2 of Bjorken and Drell and most
modern treatments). In relativistic QFT, all particles (and antiparticles)
travel forward in time, corresponding to timelike or lightlike momenta.
(Only 'virtual' particles may have unrestricted momenta; but these are
unobservable artifacts of perturbation theory.) The need for antiparticles
is in QFT instead revealed by the fact that they are necessary to construct
operators with causal (anti)commutation relations, in connection with the
spin-statistic theorem. See, e.g., Volume 1 of Weinberg's QFT book. Thus
talking about particles traveling backward in time, the Dirac sea, and holes
as positrons is outdated; it is today more misleading than it does
good. -------------------------------------------------- What about
particles faster than light
(tachyons)? -------------------------------------------------- Tachyons are
hypothetical particles with speed exceeding the speed of light. Special
relativity demands that such particles have imaginary rest mass (negative
m^2), and hence can never be brought to rest (or below the speed of light);
unlike ordinary particles, they speed up as they lose energy, Charged
tachyons produce Cerenkov radiation which has never been observed. (However,
Cerenkov radiation is indeed observed when fast particles enter a dense
medium in which the speed of light is smaller than the particle's speed.
Relativitly only demands that no particle with real mass is faster than the
speed of light in vacuum.) Neutrinos are uncharged and have a squared mass
of zero or very close to zero, and hence could possibly be tachyons.
Recently observed neutrino oscillations confirmed a small squared mass
difference between at least two species of neutrinos. This does not yet
settle the sign of m^2 for any species. Direct measurements of m^2 have
experimental errors still compatible with m^2=0. For data see
http://cupp.oulu.fi/neutrino/ The initial interest in tachyons stopped
around 1980, when it was clear that the QFT of tachyons would be very
different from standard QFT, and that experiment didn't demand their
existence. In fact, the theory of symmetry breaking demands that tachyons do
_not_ exist: When a relativistic field theory is deformed in a way that the
square of the mass (pole of the S-matrix) of some physical particle would
cross zero, the old physical vacuum becomes unstable and induces a phase
transition to a new physical vacuum in which all particles have real
nonnegative mass. This would happen already at tiny negative m^2, and is
believed to be the cause of inflation in the early universe. (Of course, the
exact mechanism is not known since it would require a nonperturbative
definition of QFT. But classical and semiclassical computations strongly
suggest the correctness of this picture.) Expanding a theory (such as the
standard model) around an unstable state (e.g., the Higgs with a local
maximum at vanishing vacuum expectation) formally produces a bare tachyon.
This does not contradict the above assertion. Asymptotic power series
expansions around maxima (especially those with tiny or vanishing
convergence radius) make meaningless assertions about the behavior of a
function near one of its minima. Since physical particles arise from field
excitations near the global minimum of the effective energy, perturbations
around the maximum are unphysical. An expansion around an unstable state
gives no significant information, unless one has a system that actually _is_
close such an unstable state (as perhaps the very early universe). But in
that case there are no relevant excitations (tachyons), since the whole
process (inflation) of motion towards a more stable state proceeds so
rapidly that excitations do not form and everything can be analyzed
semiclassically. The physical Higgs field is far away from the unstable
maximum, and its particle excitations have a positive real mass, hence are
not tachyons. Below are some references about tachyons. the more important
papers are marked by an asterisk. * G. Feinberg, Possibility of
Faster-Than-Light Particles, Phys. Rev. 159, 1089 (1967). J. Dhar and E. C.
G. Sudarshan, Quantum Field Theory of Interacting Tachyons, Phys. Rev. 174,
1808-1815 (1968) M. Glück, Note on Causal Tachyon Fields, Phys. Rev. 183,
1514 (1969). D. G. Boulware, Unitarity and Interacting Tachyons, Phys. Rev.
D 1, 2426 (1970). * B. Schroer, Quantization of m^2<0 Field Equations, Phys.
Rev. D 3, 1764 (1971). G. Feinberg Lorentz invariance of tachyon theories
Phys. Rev. D 17, 1651 (1978) C. Schwartz Some improvements in the theory of
faster-than-light particles Phys. Rev. D 25, 356 (1982) SM. B. Davis, M. N.
Kreisler, and T. Alväger Search for Faster-Than-Light Particles Phys. Rev.
183, 1132 (1969) * L. W. Jones A review of quark search experiments Rev.
Mod. Phys. 49, 717 (1977) [Section IIIG reviews the vain search for
tachyons.] The Wikipedia entry for tachyons,
http://en.wikipedia.org/wiki/Tachyon gives some more explanations.
http://www.weeklyscientist.com/ws/articles/tachyons.htm speculates about
connections between tachyons and inflation, but has some links with further
useful information. ------------------------ Summing divergent
series ------------------------ Most perturbation series in QFT are believed
to be asymptotic only, hence divergent. Strong arguments (which haven't lost
in half a century their persuasive power) supporting the view that one
should expect the divergence of the QED (and other relatvistic QFTs) power
series for S-matrix elements, for all values of alpha0 (and independent of
energy) are given in F.J. Dyson, Divergence of perturbation theory in
quantum electrodynamics, Phys. Rev. 85 (1952), 613--632. However, one can
one still extract information by resumming techniques. With experimental
results you just have numbers, and not infinite series, so questions of
convergence do not occur. On the other hand, if you know of an infinite
series a finite number of terms only, the result can be, strictly speaking,
anything. But usually one applies some extrapolation algorithm (e.g., the
epsilon or eta algorithm) to get a meaningful guess for the limit, and
estimates the error by doing the same several times, keeping a variable
number of terms. The difference between consecutive results can count as a
reasonable (though not foolproof) error estimate of these results.
Similarly, given a finite number of coefficients of a power series, one can
use Pade approximation to find an often excellent approximation of the
'intended' function, although of course, a finite series says, strictly
speaking, nothing about the limit of the sequence. But to have reliable
bounds you need to know an exact definition of what you are approximating,
and work from there. One can study these things quite well with functions
which have known asymptotic expansions (e.g., Watson's lemma). In many cases
(and under well-defined conditions), the resulting infinite series is Borel
summable. To sum f(x) = sum a_k x^k (1) if it is divergent or very slowly
convergent, you can sum instead its Borel transform Bf(x) = sum a_k/k! x^k
(2) which obviously converges much faster (if not yet, you could probably
repeat the procedure). under certain assumptions on f, stronger than simply
asserting that (1) is an asymptotic expansion for f (but including the case
where (1) has a positive radius of convergence), one can show that f can be
reconstructed from Bf by means of some integral transform. In certain cases,
where nonperturbative QM applies, one can show that the nonperturbative
result satisfies the properties needed to show that Borel summation of the
perturbative expansion reproduces the nonperturbative result. See also the
thread Re: unsolved problems in QED starting with
http://www.lns.cornell.edu/spr/2003-03/msg0049669.html ---------------------
-------------- Nonperturbative computations in
QFT ----------------------------------- There is well-defined theory for
computing contributions to the S-matrix in QED (and other renormalizable
field theories) by perturbation theory. There is also much more which uses
handwaving arguments and appeals to analogy to compute approximations to
nonperturbative effects. Examples are: - relating the Coulomb interaction
and corrections to scattering amplitudes and then using the nonrelativistic
Schroedinger equation, - computing Lamb shift contributions (now usually
done in what is called the NRQED expansion), - Bethe-Salpeter and
Schwinger-Dyson equations obtained by resumming infinitely many diagrams.
The use of 'nonperturbative' and 'expansion' together sounds paradoxical,
but is common terminology in QFT. The term 'perturbative' refers to results
obtained directly from renormalized Feynman graph evaluations. From such
calculations, one can obtain certain information (tree level interactions,
form factors, self energies) that can be used together with standard QM
techniques to study nonperturbative effects - generally assuming without
clear demonstrations that this transition to QM is allowed. Of course,
although usually called 'nonperturbative', these techniques also use
approximations and expansions. The most conspicous high accuracy
applications (e.g. the Lamb shift) are highly nonperturbative. But on a
rigorous level, so far only the perturbative results (coefficients of the
expansion in coupling constants) have any validity. Although the
perturbation series in QED are believed to be asymptotic only, one can get
highly accurate approximations for quantities like the Lamb shift. However,
the Lamb shift is a nonperturbative effect of QED. One uses an expansion in
the fine structure constant, in the ratio electron mass/proton mass, and in
1/c (well, different methods differ somewhat). Starting e.g., with Phys.
Rev. Lett. 91, 113005 (2003) you'd be able to track the literature.
Perturbative results are also often improved by partial summation of
infinite classes of related diagrams. This is a standard approach to go some
way towards a nonperturbative description. Of course, the series diverges
(in case of a bound state it _must_ diverge, already in the simplest,
nonrelativistic examples!), but the summation is done on a formal level (as
everything in QFT) and only the result reinterpreted in a numerical way. In
this way one can get in the ladder approximation Schroedinger's equation,
and in other approximations Bethe-Salpeter equations, etc. See Volume 1 of
Weinberg's QFT
book. ---------------------------------------------------------- Functional
integrals, Wightman functions, and rigorous
QFT ---------------------------------------------------------- QFT assumes
the existence of interacting (operator distribution valued) fields Phi(x)
with certain properties, which imply the existence of distributions
W(x_1,...,x_n)=<0Phi(x_1)...Phi(x_n)0. But the right hand side makes no
rigorous sense in traditional QFT as found in most text books, except for
free fields. Axiomatic QFT therefore tries to construct the W's - called the
Wightman functions - directly such that they have the properties needed to
get an S-matrix (Haag-Ruelle theory), whose perturbative expansion can be
compared with the nonrigorous mainstream computations. This can be done
successfully for many 2D theories and for some 3D theories, but not, so far,
in the physically relevant case of 4D. To construct something means to prove
its existence as a mathematically well-defined object. Usually this is done
by giving a construction as a sort of limit, and proving that the limit is
well-defined. (This is different from solving a theory, which means
computing numerical properties, often approximately, occasionally - for
simple problems - in closed analytic form.) To compare it to something
simpler: In mathematics one constructs the Riemann integral of a continuous
function over a finite interval by some kind of limit, and later the
solution of an initial value problem ordinary differential equations by
using this and a fixed point theorem. This shows that each (nice enough)
initial value problem is uniquely solvable. But it tells very little of its
properties, and in practice no one uses this construction to calculate
anything. But it is important as a mathematical tool since it shows that
calculus is logically consistent. Such a logical consistence proof of any 4D
interacting QFT is presently still missing. Since logical consistency of a
theory is important, the first person who finds such a proof will become
famous - it means inventing new conceptual tools that can handle this
currently intractable problem. Wightman functions are the moments of a
linear functional on some algebra generated by field operators, and just as
linear functionals on ordinary function spaces are treated in terms of
Lebesgue integration theory (and its generalization), so Wightman linear
functionals are naturally treated by functional integration. The 'only'
problem is that the latter behaves much more poorly from a rigorous point of
view than ordinary integration. Wightman functions are the moments of a
positive state on noncommutative polynomials in the quantum field Phi, while
time-ordered correlation functions are the moments of a complex measure on
commutative polynomials in the classical field Phi. In both cases, we have a
linear functional, and the linearity gives rise to an interpretation in
terms of a functional integral. The exponential kernel in Feynman's path
integral formula for the time-ordered correlation functions comes from the
analogy between (analytically continued) QFT and statistical mechanics, and
the Wightman functions can also be described in a similar analogy, though
noncommutativity complicates matters. The main formal reason for this is
that a Wick theorem holds both in the commutative and the noncommutative
case. For rigorous quantum field theory one essentially avoids the path
integral, because it is difficult to give it a rigorous meaning when the
action is not quadratic. Instead, one only keeps the notion that an integral
is a linear functional, and constructs rigorously useful linear functionals
on the relevant algebras of functions or operators. In particular, one can
define Gaussian functionals (e.g., using the Wick theorem as a definition,
or via coherent states); these correspond exactly to path integrals with a
quadratic action. If one looks at a Gaussian functional as a functional on
the algebra of fields appearing in the action (without derivatives of
fields), one gets - after time-ordering the fields - the traditional path
integral view and the time-ordered correlation functions. If one looks at it
as a functional on the bigger algebra of fields and their derivatives, one
gets - after rewriting the fields in terms of creation and annihilation
operators - the canonical quantum field theory view with Wightman functions.
The algebra is generated by the operators a(f) and a^*(f), where f has
compact support, but normally ordered expressions of the form S = integral
dx : L(Phi(x), Nabla Phi(x)) : make sense weakly (i.e., as quadratic forms).
The art and difficulty is to find well-defined functionals that formally
match the properties of the functionals 'defined' loosely in terms of path
integrals. This requires a lot of functional analysis, and has been
successfully done only in dimensions d<4. For an overview, see: A.S.
Wightman, Hilbert's sixth problem: Mathematical treatment of the axioms of
physics, in: Mathematical Developments Arising From Hilbert Problems, edited
by F. Browder, (American Mathematical Society, Providence, R.I.) 1976,
pp.147-240. ---------------------------------------------------- Is there a
rigorous interacting QFT in 4
dimensions? ---------------------------------------------------- In spite of
many attempts (and though numerous uncontrolled approximations are routinely
computed), no one has so far succeeded in rigorously constructing a single
QFT in 4D which has nontrivial scattering. Not even QED is a mathematical
object, although it is the theory that was able to reproduce experiments
(Lamb shift) with an accuracy of 1 in 10^12, and with less accuracy already
in 1948. But till today no one knows how to formulate the theory in such a
way that the relevant objects whose approximations are calculated and
compared with experiment are logically well-defined. See, e.g., the S.P.R.
threads http://groups.google.com/groups?q=Un...roblems+in+QED
http://groups.google.com/groups?q=Wh...defined+in+QED This probably
explains the high prize tag of 1.000.000 US dollars, promised for a solution
to one of the Clay millenium problems, that asks to find a valid
construction for d=4 quantum Yang-Mills theories that is strong enough to
prove correlation inequalities corresponding to the existence of a mass gap.
The problem is to explain rigorously why the mass spectrum for compact Yang
Mills QFT begins at a positive mass, while the classical version has a
continuous spectrum beginning at 0. The state of the art at the time the
problem was crowned by a prize is given in
http://www.claymath.org/Millennium_P...objects/Offici
al_Problem_Description.pdf I don't think significant progress has been
published since then. Yang-Mills theories are (perhaps erroneously) believed
to be the simplest (hopefully) tractable case, being asymptotically complete
while not having the extra difficulties associated with matter fields.
(There are only gluons, no quarks or leptons.) Of course, one would like to
show rigorously that QED is consistent. But QED has certain problems (the
Landau pole, see below) that are absent in so-called asymptotically free
theories, of which Yang-Mills is the simplest. Note that rigorous
interacting relativistic theories in 2D and 3D exist; see, e.g., Glimm and
Jaffe's ''Quantum Physics: A Functional Integral Point of View''. This book
is quite difficult on first reading. Volume 3 of Thirring's Course in
Mathematical Physics (which only deals with nonrelativistic QM but in a
reasonably rigorous way) might be a good preparation to the functional
analysis needed. A more leisurely introduction of the physical side of the
matter is in Elcio Abdalla, M. Christina Abdalla, Klaus D. Rothe
Non-Perturbative Methods in 2 Dimensional Quantum Field Theory World
Scientific, 1991, revised 2nd. ed. 2001.
http://www.wspc.com/books/physics/4678.html The book is about rigorous
results, with a focus on solvable models. Note that 'solvable' means in this
context 'being able to find a closed analytic expression for all S-matrix
elements'. These solvable models are to QFT what the hydrogen atom is to
quantum mechanics. The helium atom is no longer 'solvable' in the present
sense, though of course very accurate approximate calculations are possible.
Unfortunately, solvable models appear to be restricted to 2 dimensions. The
deeper reason for the observation that dimension d=2 is special seems to be
that in 2D the line cone is just a pair of lines. Thus space and time look
completely alike, and by a change of variables (light front quantization),
one can disentangle things nicely and find a good Hamiltonian description.
This is no longer the case in higher dimensions. (But 4D light front
quantization, using a tangent plane to the light cone, is well alive as an
approximate technique, e.g., to get numerical results from QCD.) Thus, while
2D solvable models pave the way to get some rigorous understanding of the
concepts, they are no substitute for the functional analytic techniques
needed to handle the non-solvable models such as Phi^4
theory. ------------------ Is QED consistent? ------------------ Many
physicists think that QED cannot be a consistent theory, although it gives
the most accurate predictions modern physics has to offer, namely that of
the Lamb shift. But there is a phenomenon called the Landau pole that
indicates that at extremely large energies (far beyond the range of physical
validity of QED) something might go wrong with QED. This is probably why
Yang=Mills and not QED was chosen as the model theory for the millenium
prize. Since the existence of the Landau pole is confirmed only in low order
perturbation theory and in lattice calculations, hep-lat/9801004 and
hep-th/9712244 this observation has currently no rigorous mathematical
substance. Moreover, the quality of the computed approximations are a strong
indication that there should be a consistent mathematical foundation (for
not too high energies), although it hasn't been found yet. There is no
indication at all that at the energies where QED suffices to describe our
world (with electrons and nuclei considered elementary particles), it should
be inconsistent. To show this rigorously, or to disprove therefore remains
another unsolved (and for physics more important) problem. Perturbative QED
is only a rudimentary version of the 'real QED'; which can be seen that
Scharf's results on the external field case are much stronger (he constructs
in his book the S-matrix) than those for QED proper (where he only shows the
existence of the power series in alpha, but not their convergence). The
quest for 'existence' of QED is the quest for a framework where the formulas
make sense nonperturbatively, and where the power series in alpha is a
Taylor expansion of a (presumably nonanalytic) function of alpha that is
mathematically well-defined for alpha around 1/137 and not too high energy.
This is still open. More precisely: Probably the QED S-matrix exists
nonperturbatively for alpha <= 1/137 and input energies <= some number
E_limit(alpha) larger than the physical validity of pure QED. What is needed
is a mathematical proof that the QED S-matrix exists for 0

posted by Kirk Gregory Czuhai @ 10:57 AM 0 comments

more physics PHUN 4u !!!
------------------------- A theoretical physics
FAQ -------------------------
http://www.mat.univie.ac.at/~neum/physics-faq.txt Here are answers to some
frequently asked questions from theoretical physics. They were collected
from my answers to postings to the newsgroup sci.physics.research. Of course
they refer only to a tiny part of theoretical physics, and they are only as
good as my understanding of the matter. This doesn't mean that they are
poor... But if you have suggestions for improvements, please write me at
Arnold.Neumaier@univie.ac.at If you have questions, please post them to the
newsgroup sci.physics.research (http://www.lns.cornell.edu/spr)! Happy
Reading! Arnold Neumaier University of Vienna
http://www.mat.univie.ac.at/~neum/ Abbreviations: QM = quantum mechanics.
QFT = quantum field theory. QED = quantum electrodynamics. s.p.r =
sci.physics.research (newsgroup). Strings like quant-ph/0303047 refer to
electronic documents in the e-Print archive (see
http://xxx.lanl.gov/). ----------------- Table of Contents -----------------
(The labels may change with time as answers to further questions will be
added. So, to quote part of the FAQ, refer to the title of a section and not
to its label.) 1a. Are electrons pointlike/structureless? 1b. What are
'bare' and 'dressed' particles? 1c. How meaningful are single Feynman
diagrams? 1d. How real are 'virtual particles'? 1e. What is the meaning of
'on-shell' and 'off-shell'? 1f. Virtual particles and Coulomb interaction
1g. Are virtual particles and decaying particles (resonances) the same? 1h.
Can particles go backward in time? 1i. What about particles faster than
light (tachyons)? 2a. Summing divergent series 2b. Nonperturbative
computations in QFT 2c. Functional integrals, Wightman functions, and
rigorous QFT 2d. Is there a rigorous interacting QFT in 4 dimensions? 2e. Is
QED consistent? 2f. Bound states in relativistic QFT 2g. Why bother about
rigor in physics? 2h. Why normal ordering? 3a. Is there a multiparticle
relativistic quantum mechanics? 3b. Localization and position operators 3c.
Representations of the Poincare group, spin and gauge invariance 4a. A
concise formulation of the measurement problem of QM 4b. The double slit
experiment 4c. The Stern-Gerlach experiment 4d. The minimal interpretation
4e. The preferred basis problem 4f. Does decoherence solve the measurement
problem? 4g. Which interpretation of quantum mechanics is most consistent?
4h. What about relativistic measurement theory? 5a. Random numbers in
probability theory 5b. How meaningful are probabilities of single events?
5c. How do probabilities apply in practice? 5d. Priors and entropy in
probability theory 6a What are bras and kets? 6b. What is the meaning of the
entries of a density matrix? 7a. What is the tetrad formalism? 7b. Energy in
general relativity 7c. Difficulties in quantizing gravity 7d. Is quantum
mechanics compatible with general relativity? 7e. Why do gravitons have spin
2? 8a. Theoretical challenges close to experimental data 98a. Background
needed for theoretical physics 99a.
Acknowledgments -------------------------------------- Are electrons
pointlike/structureless? -------------------------------------- Both
electrons and neutrinos are considered to be pointlike as bare particles,
because of the way they appear in the standard model. But physical,
relativistic particles are not pointlike. An intuitive argument for this is
the fact that their localization to a region siognificantly smaller than the
de Broglie wavelength would need energies larger than that needed to create
particle-antiparticle pairs, which changes the nature of the system. (See
also this FAQ about localization, and Foldy's papers quoted there.) On a
more formal, quantitative level, the physical, dressed particles have
nontrivial form factors, due to the renormalization necessary to give finite
results in QFT. Nontrivial form factors give rise leading to a positive
charge radius. In his book S. Weinberg, The quantum theory of fields, Vol.
I, Cambridge University Press, 1995, Weinberg defines and explicitly
computes in (11.3.33) the 'charge radius' of a physical electron. But his
formula is not fully satisfying since it is not fully renormalized (infrared
divergence: the expression contains a ficticious photon mass, and diverges
if this goes to zero). (28) in hep-ph/0002158 = Physics Reports 342, 63-26
(2001) handles this using a binding energy dependent cutoff, which makes the
electron charge radius depend on its surrounding. The paper L.L. Foldy,
Neutron-electron interaction, Rev. Mod. Phys. 30, 471-481 (1958). discusses
the extendedness of the electron in a phenomenological way. On the numerical
side, I only found values for the charge radius of the neutrinos, computed
from the standard model to 1 loop order. The values are about 4-6 10^-14 cm
for the three neutrino species. See (7.12) in Phys. Rev. D 62, 113012 (2000)
http://adsabs.harvard.edu/cgi-bin/np...hDT.......130L gives in
an abstract of a 1982 thesis of Anzhi Lai an electron charge radius of ~
10^{-16} cm (But I haven't seen the thesis.) The "form" of an elementary
particle is described by its form factor, which is a well-defined physical
function (though at present computable only in perturbation theory)
describing how the (spin 0, 1/2, or 1) particle's response to an external
classical electromagnetic field deviates from the Klein-Gordon, Dirac, or
Maxwell equations, respectively. In Foldy's paper, the form factors are
encoded in the infinite sum in (16). The sum is usually considered in the
momentum domain; then one simply gets two k-dependent form factors, where k
represents the 4-momentum transferred in the interaction. These form factors
can be calculated in a good approximation perturbatively from QFT, see for
example Peskin and Schroeder's book. An extensive discussion of form factors
of Dirac particles and their relation to the radial density function is in
D. R. Yennie, M. M. Levy and D. G. Ravenhall, Electromagnetic Structure of
Nucleons, Rev. Mod. Phys. 29, 144-157 (1957). and R. G. Sachs High-Energy
Behavior of Nucleon Electromagnetic Form Factors Phys. Rev. 126, 2256-2260
(1962) For proton and neutron form factors, see hep-ph/0204239 and
hep-ph/0303054 ---------------------------------------- What are 'bare' and
'dressed' particles? ---------------------------------------- A bare
electron is the formal entity discussed in textbooks when they do
perturbative quantum electrodynamics. The intuitive picture generally given
is that a bare electron is surrounded by a cloud of virtual photons and
virtual electron-positron pairs to make up a physical, 'dressed' electron.
Only the latter is real and observable. The former is a formal caricature of
the latter, with paradoxical properties (infinite mass, etc.). On a more
substantial level, the observable electrons are produced from the bare
electrons by a process called renormalization, which modifies the
propagators by self-energy terms and the currents by form factors. As the
name says, the latter define the 'form' of a particle. (In the above
picture, it would correspond to the shape of the virtual cloud, though it is
better to avoid giving the virtual particles too much of meaning.) The
dressed object is the renormalized, physical object, described
perturbatively as the bare object 'clothed' by the cloud of virtual
particles. The dressed interaction is the 'screened' physical interaction
between these dress objects. To draw an analogy in nonrelativistic QM think
of nuclei as bare atoms, electrons as virtual particles, atoms as dressed
nuclei and the residual interaction between atoms, computed in the
Born-Oppenheimer approximation, as the dressed interaction. Thus, for Argon
atoms, the dressed interaction is something close to a Lennard-Jones
potential, while the bare interaction is Coulomb repulsion. This is the
situation physicists had in mind when they invented the notions of bare and
dressed particles. Of course, it is only an analogy, and should not be taken
very seriously. It just explains the intuition about the terminology used.
The electrons in QM are real, physical electrons that can be isolated. The
reason is that they are good eigenstates of the Hamiltonian. On the other
hand, virtual particles don't have this nice attribute since the
relativistic Hamiltonian H from field theory contains creation and
annihilation operators which mess things up. The bare particles correspond
to 1-particle states in the Hilbert space (though that is not quite true
since there is no good Hilbert space picture in conventional interacting
QFT). Multiplying them with H introduces terms with other particle numbers,
hence a bare particle can never be an eigenstate of H, and thus never be
observable in the way a nonrelativistic particle is. The eigenstates of the
relativistic Hamiltonian are, instead, complicated multibody states
consisting of a superposition of states with any number of particles and
antipar