well we're approaching halloween it's uh
and it's that time of year when we have
to think about spooky things and brady
you've set us the challenge in physics
of coming up with something
physically that can represent halloween
not easy
but in the world of particle physics
which is a rather unusual world we have
ghost particles
well ghost particles they're bad things
right they're really bad things
they can be good and they can be bad the
difference between the good ones and the
bad ones is that the the good ones don't
exist as real particles they're just
virtual particles so you can't just grab
one whereas the bad ones do and
some of them
make a theory consistent and others
completely destabilize a theory and so
the good ones make the theory consistent
and if you have the bad ones then the
theory becomes inconsistent and usually
is thrown out let's talk about the good
ones first
in particle physics we deal with very
small things we're interested in
interactions and so we might have a
group of particles initially which
interact to give me a group of particles
at the end and they don't have to be the
same but what we're interested in is a
way of describing that interaction to go
from this initial state to the final
state
and there are a number of approaches to
that and one of the most famous that's
been developed
initially by dirac but then really
pushed forward by a feynman was called
the path integral formalism
so we have various ways of doing it
there might be one path that will take
me this way but perhaps it's not unique
maybe there's another way of getting to
that state and i'll goes up here and
comes down maybe goes down here and
comes up in fact there's an infinite
number of ways of doing this
and what feynman said was if you want to
work out the actual amplitude or the
probability of starting here and ending
here you can't just take what is called
the classical path the path that we're
used to
from classical mechanics like mutant
holders you have to include all of these
other weird and wonderful trajectories
now we want to just use the path
interval to describe real physics we
want to be able to use it to describe
the interactions the forces that we're
used to electromagnetism
we want to understand the weak force you
know why is the sun burning we want to
understand the strong force why why is
the nucleus of the atom bound together
why don't the protons blow themselves
apart why they bound together why are
quarks bound together
this requires us to understand an area
of particle physics called gauge
theories uh well what the good ones do
is they they eat up uh other things that
are on physical so in physics you have
um theories which have lots of symmetry
so you can you want lots of things look
the same so there's lots of sort of
redundant ingredients and what the the
good ghosts come along and do is they
they eat them up essentially but they
don't exist as real particles so they
don't actually
screw with the uh with the real world
they just they just help us to quantize
certain types of theory gauge theories
you introduce the ghost particles and
they cancel out all the extra ones
leaving you with just the physical ones
left and so it's a way of regularizing
your theory and making it
self-consistent so these are the good
particles
yeah i guess they're really in this case
they really are just a mathematical
trick because as i say you've got you've
got these theories which have these
symmetries these redundancies of
information
and you've got to when you actually
quantize the theory you've got to remove
those redundancies and use this
mathematical trick of introducing this
ghost particle
that comes along
sees the the extra degrees of freedom
the extra redundant bits
and eats them
and then they're gone so you're just
left with what's physical
are ghost particles real things no but
if ghost particles do something they
make something work then surely they
must exist
so the the ghost particles that that are
needed for the consistency of this model
are virtual particles they they will
they take part in an interaction
but you'll ne you're never able to
actually pin them down so they're never
part of the final state if if you say
what does an experiment measure an
experiment measures an initial state and
some final state and then things happen
in between the ghost particles pop up
and disappear again in that inter
intervening period they're definitely
there in sense of their virtual
particles that pop up and disappear
again but they're not there in the sense
of you detecting them so are they
actually particles why do you give them
the name particle
because they have properties that are
similar to particles you you can
associate various numbers with them you
can associate a momentum with them you
can associate a mass with them if it
turns out these um
gauge fields that we were describing
acquire a mass which they do and and
what's known as the higgs symmetry
breaking phase transition where all
particles acquire mass these particles
will also acquire a mass they have many
properties of of conventional particles
it's just that you they're the virtual
ones that
link you from your initial state to your
final state that sounds really
wishy-washy to me that sounds like
something humans have made up
to cover for something they don't
understand no no not at all it's not
wishy-washy remember
what the ghost particles are there to to
ex to help
make this path integral approach um
consistent but maybe the path integral
approach is wrong
huge huge questions about the path
integral approach indeed
for mathematicians
uh it's not a very well defined concept
uh
for various reasons it's it's not that
well defined
physically it's brilliant it works
amazingly well it produces fantastic
accuracy in terms of comparing
theoretical predictions of quantum
electrodynamics
electroweak theory comparing it with
observations oh the bad case well they
really are bad so these are bad so the
crucial difference between these and the
other ones is that is that they
basically that they can exist as real
particles
and what's so bad about them is if you
wanted to be quantum mechanically
consistent
then they have to carry negative kinetic
energy and that's really bad so what
that means is essentially you know if
you and i were to was to run along on
the football field as we as we have in
the past there brady and you know we the
faster we run the more kinetic energy
we have
if a ghost particle was doing that he
would have more negative kinetic energy
the faster he ran the more negative his
kinetic energy would become at school
we're taught that the energy is usually
made up of the kinetic energy that's the
energy of movement plus the potential
energy
and you always think of these as
positive so if you just take this this
little blob of space here right right in
front of me
then you could produce on the one hand
you could produce a an ordinary particle
like an apple and that's carrying
negative that's moving around that's
carrying positive energy but at the same
time you could produce a ghost to
produce the apple and the ghost the
apple carries positive kinetic energy
the ghost carries negative kinetic
energy and the two together cancel each
other out
right so you could actually produce
these without any cost and energy these
fluctuations these ghost-like particles
and they're called ghosts because of the
negative kinetic energy these ghost-like
particles
can be coupled to other particles and
you'd at no at
no cost you just keep producing ghost
particles and these extra particles you
just bombard the universe with these
extra particles
so there's nothing to stop that
happening and actually what happens is
these will constantly get produced in
these two pairs okay produce the apples
and the ghosts the abs on the ghost and
it'll happen everywhere and eventually
the room will be rapidly filled up with
well positive energy apples and negative
energy ghosts and you completely have an
unstable situation and that is that's an
instability in the theory that solution
you've got is clearly an unstable one it
doesn't want to stay there and so people
tend to use this criteria this existence
of this ghost particle in this second
version as a as an instability in the
theory and you discard the theory so
yeah your theory might predict their
existence if it does it's a bad
prediction it's not a prediction you
want for your theory