The holy grail of theoretical physics is to come  up with a quantum theory of gravity.

But after   a century of trying we really have no idea how  close we are, or it it's even possible.

But we   shouldn't feel bad because it turns out that  the universe is doing everything it its power   to make this as difficult as possible.

Or perhaps it's just telling us that quantum gravity is not 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 3 of the 4 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 quanta–gravity   should be mediated by it’s 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 to test our 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 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 possible to detect   a graviton–something we’d need to do in order to  verify that gravity is really quantum.

But first,   we’re going to follow another musing of Dyson’s,  in which he asks whether the same trick that   told us electromagnetism must be a quantum  force and 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 Planck 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 indivisible packets of energy that  we call photons.

Planck and Einstein’s   discoveries were the clues that led to the full  development of quantum mechanics in the mid 1920s,   which was followed quickly by our full quantum theory  of electromagnetism–quantum electrodynamics.

But even before electromagnetism was  properly quantized, Neils Bohr & Léon   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 the 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 measure the other.

The Heisenberg  uncertainty principle is a fundamental limit   to the knowability of the quantum world, and we  talk about this fundamentalness in this video.

This tradeoff between the knowledge we can possess  about a quantum system applies to many pairs of   properties–position versus momentum, energy  versus time, one axis of polarization or spin   versus a perpendicular axis, and many more.

So if  the electromagnetic field is quantum in nature,   the uncertainty principle should apply  to our attempts to measure this field.

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 like 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’ motion is entirely defined   by their interactions via the electromagnetic  field.

So Bohr and Rosenfeld argued that the   same restrictions on the measurement of particle  motion have to apply to the field that governs   that motion.

After all, measurement 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 turned out to be.

OK, 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 Bohr-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   two particles.

The interaction needs to  be mediated by the most “quantum” possible   influence of the EM field–a so-called quantum  of action.

That’s the part of the EM field   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 Bohr 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 pairs 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 the 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 Bohr 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 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 Bohr 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.

OK, 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 ripples 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 alternately stretched  and compacted by a very tiny amount.

At least that’s how gravitational waves look in  general relativity–Einstein’s very un-quantum   theory of gravity.

In classical electromagnetism,  electromagnetic waves are caused by accelerating   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 of many gravitons.

In 2015 we detected our first gravitational  waves caused by the mergers of black holes with   the Laser Interferometer Gravitational Wave  Observatory.

The two LIGO facilities sensed   the extremely tiny relative changes in lengths  between their 4-km arms by bouncing lasers many   times along each arm and watching for subtle  changes in how those laser beams recombined.

So what would it take to measure a single  graviton?

Probably it’s quite a bit more   difficult than measuring a single photon, but  there must be some far-future gravitational   wave detector that could do it.

That’s what  Dyson wanted to find out.

We’ll start by   estimating how many gravitons are in a typical  gravitational wave like the ones detected by LIGO.

If we wanted to do that for  an electromagnetic wave,   we’d take the total energy of the wave and  divide it by the energy of a single photon,   which is just the Planck constant times its  frequency.

That tells us that a piddling   5 milliWatt 630nm red laser pointer  blasts out 10^16 photons per second.

The typical gravitational wave detectable by  LIGO has an energy density of approximately   10^-11 Joules per cubic meter and angular  frequency of 1 kilohertz (that's 1000 hertz).

According to Dyson the energy density of  a single graviton in this frequency is   at most 310^-48 Joules per cubic meter.

That gives us around 3x10^37 gravitons   per cubic meter in these waves.

So what  would it take to detect just one of these?

Well, if the gravitational wave I described with   around 10^37 gravitons and that's just at  the edge of LIGO’s sensitivity,   then we’d need to improve that sensitivity  by a factor of 10^37.

That sounds challenging–but   surely not impossible, even if it would take  some science-fiction-level device to do it.

To see 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 detect  the change in distance due to a single graviton,   we’d need to be able to measure a change in distance  on the order of the Planck length,   and that this requirement is actually  independent of the frequency of the graviton.

You might recall from previous videos  that the Planck length is essentially   the smallest distance 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 distance 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 the 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 now very familiar with.

While a mass is being moved by the graviton  its speed changes.

It changes roughly by the   distance it travels divided by time  it takes 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 one graviton.

So now we have an estimate for the  uncertainty in the position needed   to detect the graviton–and that just around half a Planck length–as well as   the uncertainty in 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 graviton.

It’s a simple   enough equation–the mass separation has to  be less than or equal to the gravitational   constant times the mass of the masses  divided by the speed of light squared.

But that expression is familiar to all  physicists, and is very bad in this context.

It’s the expression for the Schwarzchild radius.

Any mass compacted to a size smaller than this   radius becomes permanently trapped by its own  gravitational field.

It becomes a black hole 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   smaller than the Planck length threatens  black holes, as we’ve discussed before.

So it seems that nature isn’t just conspiring  to thwart our theoretical arguments for quantum   gravity, but also to stop us building the  detector we’d 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 for gravitational waves--but that's really  in the realm of extreme far-future technology.

There's also indirect measures of quantum gravity  in the same vein as the Bohr-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 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   hope that one day we'll find a way to test, and  maybe verify, the quantum nature of space time.