the most successful theory in all of
physics is arguably quantum field theory
it's made the most precise predictions
in all of science but it's also made the
worst
there's a massive disagreement between
the theoretical and the measured values
of the energy of the vacuum we call this
theoretical fail the vacuum catastrophe
the quantum vacuum is a seething ocean
of activity virtual particles appear and
vanish from nowhere in seeming violation
of our intuitions about the conservation
of mass and energy we saw in our recent
episode that we can thank the Heisenberg
uncertainty principle for this bizarre
behavior it tells us that there's a
quantum fuzziness and the amount of
energy contained at every point in space
a nonzero zero-point energy in the
quantum fields that can briefly manifest
as particles
this suggests that space itself contains
energy but how much energy quantum field
theory predicts that the energy of the
vacuum should be up to a hundred and
twenty orders of magnitude greater than
the measured value it's one of the
greatest unsolved problems in physics
let's talk about vacuum energy from a
theoretical standpoint from the
perspective of quantum field theory
every point in space is represented by a
quantum oscillator one from each
elementary particle type higher energy
oscillations represent the presence of
real particles however even the lowest
possible energy oscillation the one
corresponding to the absence of
particles the so called vacuum state has
some energy to satisfy the Heisenberg
uncertainty principle the vacuum state
of any field oscillation must be half of
the tiny plant constant times the
frequency of that oscillation now that's
a
miniscule amount of energy except to
properly describe a perfect vacuum every
single possible frequency mode and every
pointed space must have that amount of
energy to calculate the density of
energy of the vacuum we should add this
tiny energy over an infinite range of
frequency modes for all fields now
multiply a finite energy density no
matter how small by infinity and you get
infinite energy density we'll get back
to whether the idea of infinite vacuum
energy is actually possible it certainly
sounds a bit excessive
so maybe we can avoid let's think in
terms of the electromagnetic field what
if there's a maximum possible frequency
for virtual photons then our sum of
frequency modes would be finite now it
sounds like a hack and it sort of is but
we're getting desperate and anyway
there's an almost sensible cutoff for
photon frequency it's where photon
energy is equal to the Planck energy or
10 to the power of 19 Giga electron
volts this is where our understanding of
physics breaks down until we develop a
theory of quantum gravity we can't say
where the photons above this energy are
possible so if we add up the vacuum
energy including virtual photons all the
way up to the Planck energy we get a
finite number a very very large finite
number the energy density would be 10 to
the power of a hundred and 12 eggs per
centimeter cubed this
back-of-the-envelope estimate was first
made by John Wheeler and richard fineman
who noted that one tea cup of space with
this energy density would contain enough
energy to boil all of the oceans on the
planet yet even if vacuum energy did
have a value this high in fact even if
it were infinite we may not notice at
least according to quantum theory in
fact in both quantum mechanics and
classical mechanics a particles
equations of motion depend only on
changes in energy the zero point of the
energy scale is irrelevant as long as
the vacuum energy is the same everywhere
then it's inaccessible to us as an
energy source we're going to come back
to that point in an upcoming episode so
you'll be able to knowledgeably scoff at
zero point energy perpetual motion
machines long story short a crazily high
even infinite vacuum energy doesn't
affect the predictions of quantum field
theory just redefine the zero point to
whatever you want and you're good to go
however you can't be so cavalier with
general relativity Einstein's theory
tells us that any form of energy
produces gravity and what matters is the
absolute amount of energy not relative
deviations vacuum energy should produce
a gravitational effect and a huge vacuum
energy should produce a huge
gravitational effect that effect would
be seen in two ways an energy of space
itself should cause exponential
expansion at least in the case of an
already expanding universe
it should also massively increase the
spatial curvature of the universe now
this is all extremely unintuitive and we
spend five episodes trying to give you a
sense of why this is true now feel free
to jump down that rabbit hole if you
haven't already but the upshot is that
if vacuum energy really did have the
enormous value predicted by theory then
our gently expanding geometrically flat
universe would not exist the realization
of this fact in the early days of
quantum field theory was the beginning
of what would become the vacuum
catastrophe but it wasn't a full-blown
catastrophe yet there was still a way
out if some fields can have extremely
large positive zero point energies then
perhaps others have extremely large
negative zero point energies that cancel
them out an extension to the standard
model of particle physics called
supersymmetry may partially allow this
it gives all particles a supersymmetric
counterpart that may precisely cancel
out their vacuum
now basic supersymmetry only allows us
to cancel out photons down to the so
called electro weak energy which brings
the predicted vacuum energy down to a
mere ten to the forty seven eggs per
centimeter cubed but perhaps a yet
deeper theory allows perfect canceling
down to zero for a while
theorists assumed that something like
this must be happening meaning the
vacuum energy was really zero it was a
glimmer of hope that catastrophe could
be averted that is until we discovered
dark energy in the late 90s astronomers
discovered that the expansion of the
universe is in fact accelerating in
exactly the way we would expect from a
non zero vacuum energy now unlike the
lamb shift or the Casimir effect the
observation of accelerating expansion
allows us to measure the absolute
density of vacuum energy assuming vacuum
energy is to blame dark energy weighs in
had tensed the power of negative eight
burgers per centimeter cubed compare
that to the number predicted by quantum
field theory there's a discrepancy of
120 orders of magnitude between the two
or 55 orders of magnitude if we use the
electroweak energy cutoff instead of the
Planck energy cutoff now that is what
scientists call a catastrophe QFT can
give us an extremely high vacuum energy
or a vacuum energy of exactly zero if we
assume symmetry of positive and negative
zero points between different fields but
a very small non zero vacuum energy that
requires what we call fine-tuning
gigantic positive and gigantic negative
zero point energies would need to cancel
each other out down to a very tiny
nonzero value that sounds like a
ridiculously unlikely bit of luck if we
can't invoke symmetries a proposed
solution is the entropic one we exist in
an extremely rare universe whose
fundamental fields cancelled out there
point energies or at least enough of
them to allow life and astronomers to
evolve that would imply countless other
universes with different less
comfortable vacuum energies of course it
may be that advances in theory will
resolve this catastrophe without
requiring us to invoke the anthropic
principle in the meantime the conundrum
continues to perplex physicists and
we'll do so until we reach a deeper
understanding of the true nature of
space-time last week we talked about the
missing baryon problem and some new
observations that have found this
missing matter in the vast filaments of
the cosmic web you guys had a lot of
great questions
Lucas cook asked he asked where the
neutrinos belong to the dark sector or
the light sector well for a time it was
thought that neutrinos might actually be
dark matter until it was realized they
just don't contain enough mass nor are
they clumpy enough they're too hot to
pool into the deep dark matter wells
that we see in galaxy clusters at the
same time a neutrino don't interact
electromagnetically so there in that
sense dark however usually the Dark
Sector term is used to describe the
actual sources of dark matter and dark
energy so in that sense neutrinos aren't
part of it but these definitions are
vague so don't read too much into it
a few of you asked how matter becomes or
remained so hot in these gigantic
filaments of the cosmic web well the key
to this is that they're extremely low
density the average density in the
filaments is maybe 20 baryons of a cubic
meter this means it doesn't take much
energy to accelerate the particles to
very high speeds temperature is just a
measure of the average kinetic energy
per particle so a little bit of energy
leads to very high temperatures that
energy comes from shocks that develop as
the material flows in the gravitational
field of surrounding clusters and how do
the particles stay hot well again it's
the low density as particles essentially
never encounter each other then they
aren't bumping around and that makes it
hard to radiate away there
it da Mex asked whether it's possible to
tap into the zero-point energy or dark
energy like with the zero-point modules
in Stargate the answer is absolutely no
vacuum energy can't be used as a power
source it's not just science fiction
that abuses the vacuum this way
there's a lot of pseudoscience and
outright scams science that claims this
in fact it's worth doing an episode on
the subject stay tuned if I could write
asks if I'm the hobbit dude who hooked
up with the hot elf chick dwarf faked it
right kilee the dwarf get it right