the Holy Grail of theoretical physics is to come up with a quantum theory of
gravity but after a century of try we really have no idea how close we are or
if it's even possible but we shouldn't feel bad because it turns out that the
universe is doing everything in its power to make this as difficult as
possible well perhaps it's just telling us that quantum gravity isn't possible
should we take the
hint our modern theory of gravity was discovered a little over a century ago
with Albert Einstein's general theory of relativity and then just a little under
a century ago we discovered quantum mechanics which would become our modern
theory of everything except gravity it was an exciting decade or so for physics
but then things slowed down we've spent the following 100 years trying to
reconcile these two theories and bring them together into a single Master
Theory of Everything the most common approach to this reconciliation has been
to try to make gravity quantum after all we got a theory of quantum
electromagnetism by quantizing the electromagnetic field the result was
quantum electrodynamics in which the force of electromagnetism can be
described by the exchange of a single Quantum of this field which turns out to
be the photon the same basic procedure led to the Discovery and quantization of
the strong and weak nuclear forces with their Associated particles gluons
carrying the strong force and w and z bosons carrying the weak so if three the
four forces of nature are quantum surely quantizing gravity is an essential step
on the path to a final Theory and if the gravitational field is quantized then it
should be made up of Quant gravity should be mediated by its own Force
carrying particle we call this hypothetical particle the graviton
detection of the graviton would allow us to confirm gravity's Quantum nature and
even test out theories of quantum gravity such as string theory and loop
quantum gravity we've talked about these
theories in the past they are mathematically very dense and involve
quite a bit of speculation and some have argued that we are getting way way ahead
of ourselves with these theories So today we're going to get right back to
the basics to do that we'll follow some of the thinking of Freeman Dyson who
helped shape quantum theory from near the beginning and thought about the most
fundamental questions for all his long life we'll see what he had to say about
whether it's even imposs to detect a graviton something we need to do in
order to verify that gravity really is quantum but first we're going to follow
another musing of Dyson's in which he asks whether the same trick that told us
that electromagnetism must be a Quantum force can also be applied to gravity the
quantum nature of electromagnetism was the very first clue that led to the
quantum Revolution it first showed up in the mathematical trick that Max plank
used to explain thermal radiation and this inspired Einstein to take the
quantization of electromagnetism seriously in order to explain the
photoelectric effect now we understand that the
electromagnetic field and electromagnetic waves AKA light can be
described as being composed of countless tiny and individual packets of energy
called photons Plank and Einstein's discoveries were clues that led to the
full development of quantum mechanics in the mid 192
which was followed quickly by our full quantum theory of electromagnetism
Quantum electrodynamics but even before electromagnetism was properly quantized
Neils B and Leon Rosenfeld came up with a strong argument that this Force must
be fundamentally Quantum I'm going to go through this thought experiment because
maybe if it works for electromagnetism we can also use it to argue for gravity
being Quantum let's start with a simple particle in motion at any point in time
particle has a position and a momentum if this is a Quantum particle then it's
impossible to simultaneously measure both of these properties with perfect
Precision if we try to measure the position very precisely then the
uncertainty in the momentum increases if we try to measure the momentum as
perfectly as possible then the position becomes undefined and it's not just that
we lost the certainty in one property by bumping it or whatever when we tried to
or the other the Heisenberg uncertainty principle is a fundamental limit to the
knowability of the quantum world and we talk about this fundamental in this
video this trade-off between the knowledge we can possess about a Quantum
system applies to many pairs of properties position versus momentum
energy versus time one AIS of polarization or spin versus a
perpendicular axis and many more so if the electromagnetic field is quantum in
nature then concy principle should apply to our attempts to measure this field
okay back to our particle in fact let's have two particles and give them both a
negative electric charge we start them off moving towards each other we know
that light charges repel so these particles will interact by the
electromagnetic field when they get close and be deflected
back we know that there's a Quantum restriction on how precisely we can
measure the position and momentum of these particles but we also know that
the particles motions are entirely defined by their interactions via the
electromagnetic field so bour and rosenell argued that the same
restrictions on measurement of particle motion have to apply to the field that
governs that motion after all measurements of the electromagnetic
field can only happen by observing its interactions if those interactions are
subject to fundamental Quantum uncertainty then the field must be
also and if that's true then it's reasonable to think that the
electromagnetic field is truly a Quantum entity as indeed it turns out to be okay
so if this argument applies to electromagnetism why can't it also apply
to the gravitational field if we can only measure the gravitational field
through the interaction of massive particles and those particles are
subject to Quantum uncertainty then surely our measurement of gravity is
subject to the same here it's important to pay attention to the details of the
bore Rosenfeld argument they realized that in order to confidently state that
the Heisenberg uncertainty principle applies to
electromagnetism we need to consider only a pristine electromagnetic
interaction between the two particles the interaction needs to be mediated by
the most Quantum possible influence of the EM field a socalled Quantum of
action that's the part of the EM field that we're trying to measure if there
are any extra bits of electromagnetic field then they'll add to our
uncertainty in measuring the field responsible for the interaction but
electromagnetism is pretty messy for example we know that moving charges
create magnetic fields those extraneous components of the EM field prevent us
from concluding that our knowledge of the EM field is limited to the same
degree as our knowledge of particle motion only with a pristine interaction
can we show that electromagnetism also obeys the Heisenberg uncertainty
principle but war and Rosenfeld came up with a clever trick to clean up the EM
field in their thought experiment instead of individual
particles moving towards each other they imagined in of particles one positive
and one negative that cancels out any electromagnetic field emerging from the
particle motion allowing us to describe the most fundamentally Quantum
interaction via the EM field and it allows us to show that the EM field
really is subject to True Quantum uncertainty but this is where we get
stuck with gravity particles with electric charge are subject to the
electromagnetic force the analogous charge for gravity is mass we can
imagine a pair of massive particles moving towards each other and
interacting via a Quantum of gravity our ability to measure that gravitational
interaction should be limited by our ability to measure the motion of those
particles but in order to show that the limit is truly the Heisenberg limit we
need to rule out complex interactions for the gravitational field just as we
did for the EM field so why not apply the same trick as B and Rosenfeld just
add an opposite gravitational charge to each particle but that means adding
negative masses and as far as we know negative Mass doesn't exist and it's not
just that we haven't discovered it yet there are very very good reasons to
believe that negative mass is fundamentally impossible its existence
would lead to Major paradoxes so it seems that the very
nature of gravity forbids us from using B and rosenfeld's argument that might on
the surface sound like a bit of bad luck but follow me through the next thought
experiment and it starts to feel like the universe is really conspiring to
prevent us from finding evidence of quantum gravity perhaps the most direct
evidence of quantum gravity would be the observation of a graviton or at least of
its effect after all the observation of the influence of individual photons in
the photoelectric effect was a pretty clear demonstration of the quantization
of electromagnetism so on to the next thought experiment from Freeman Dyson he
figured out what it would take to detect an individual graviton with a
gravitational wave detector gravitational waves are rieles in the
fabric of SpaceTime caused by Massive objects undergoing certain types of
motion when a gravitational wave passes by it causes distances to change as
space is ultimately stretched and compacted by a very tiny amount at least
that's how gravitational waves look in general relativity Einstein's very
unquity In classical electromagnetism electromagnetic waves are caused by
accelerated charges but we now know that those waves are really made up of
individual photons so if gravity is quantum then a gravitational wave should
be made up of many gravitons in 2015 we detected our first
gravitational waves caused by the merger of black holes with the laser
interferometer gravitational wave Observatory the two Lio facilities sense
the extremely tiny relative changes in the lengths between their 4 km Arms by
bouncing lasers many times along each arm and watching for subtle changes in
how those beams recombined so what would it take to
measure a single graviton probably is quite a bit more
difficult than measuring a single Photon but there must be some Far Future
gravitational W of detector that could do it that's what Dyson wanted to find
out so we'll start by estimating how many gravitons are in a typical
gravitational wave like the ones detected by
ligo if we want to do that for an electromagnetic wave we take the total
energy of the wave and divide it by the energy of a single Photon which is just
the plank constant time its frequency that tells us that a ping 5 m 630 NM red
laser pointer blasts out 10 ^ of 16 photons per second the typical
gravitational wave detectable by ligo has an energy density of approximately
10 ^ of -1 Jew per cubic M with an angular frequency of 1 khz that's 1,000
Herz according to Dyson the energy density of a single graviton in this
frequency is at most 3x 10^ -48 Jew per Cub M and that gives us around 3x 10^ 37
gravitons per cubic meter in these waves so what would it take to detect just one
of these well if the rotational wave that I described has around 10 37
gravitons and that's just at the edge of ligo sensitivity then we need to improve
that sensitivity by a factor of 10 ^ of 37 that sounds challenging but surely
not impossible even if it would take some science fiction level device to do
it to see just how science fictiony let's simplify our gravitational wave
detector we're going to detect incoming waves by measuring the change in the
distance between two masses we'll assume the masses are free floating in space
but the argument also works for masses that are fixed to a device Dyson argues
that in order to say that we detected a signal graviton we need to be able to
measure a change in distance on the order of the plank length and that this
requirement is actually independent of the frequency of the
graviton you might recall from previous videos that the plank length is
essentially the smallest distance that we can consider before the meaning of
distance and space breaks down it's a pretty small distance so what sort of
device could measure a change on that scale for our simplified gravitational
wave detector the question becomes what combination of masses and distances
between them would we need as our lonely graviton passes our detector the masses
move in and out by a tiny amount in order to be sensitive to that tiny
change in distance we need to measure the positions of each of those masses
with a Precision equal to half of that change but the Precision with which we
can measure those Mass positions is limited by the Heisenberg uncertainty
principle which by now you're very familiar with while a mass is being
moved by a graviton its speed changes it changes roughly by the distance it
travels divided by the time it takes for a single graviton to pass by that time
is just the separation of the masses divided by the speed of light that gives
us the variation in the speed during our measurement multiply that variation by
the mass itself and we get the change in momentum due to the passage of the
graviton so now we have an estimate for the uncertainty in the position needed
to detect the graviton and that's just around half the plank length as well as
the uncertainty in the momentum generated by the motion of the masses
caused by the graviton if we plug these into the Heisenberg uncertainty
principle we get a relationship between the masses and their separation in order
to be able to detect a single grow graviton it's a simple enough equation
the mass separation has to be less than or equal to the gravitational constant
time is the mass of the masses divided by the speed of light squared but that
expression is familiar to all physicists and he's very bad in this context it's
the expression for the SWA Shield radius any Mass compacted to a size smaller
than this radius becomes permanently trapped by its own gravitational field
it becomes a black coal this is really strange we found that a gravitational
wave detector capable of detecting a single graviton inevitably forms a black
hole that means even if it detects the graviton it swallows any information
about that measurement and so prohibits us from confirming the graviton really
any attempt to measure distances small than the plank length threatens black
holes as we've discussed before so it seems that nature isn't just conspiring
to th our theoretical Arguments for quantum gravity but also to stop us from
building the detector we need to test these
theories none of this means that gravity isn't really Quantum or that the
existence of the graviton can't be ever proved there are several proposals for
how to do this like searching for the extremely rare interactions with
particles of matter and gravitons but these events are going to be so rare
that it may be practically impossible to see enough of them to confidently
confirm their nature unless we could come up with a clean source of gravitons
immensely more powerful than is currently known like a laser of
gravitational waves but that's really in the realm of extreme far future
technology there are also indirect measures of quantum gravity in the same
vein as the B Rosenfeld argument for electromagnetism for example if we could
cause two particles to become Quantum entangled through a gravitational
interaction then that interaction itself would have
to be Quantum this is more promising than direct graviton detection but has
not yet been achieved and who knows perhaps nature will continue to conspire
to make new tests of quantum gravity impossible and maybe that's because
gravity isn't Quantum in the same way that the other forces are not that this
is going to stop us from continuing down the rabbit holes of speculative theories
in the hopes that one day we'll find a way to test and maybe verify the quantum
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