What If Gravity is NOT Quantum? (Script) (Patreon)

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 it's telling us that it isn't. Should we take the hint?

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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 ever 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. We now 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, 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 then 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 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 governed 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 too. 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 the 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 avoid 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 exactly 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, 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 figure 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 (1000 hertz). According to Dyson the energy density of a single graviton of 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 is just at the edge of LIGO’s sensitivity, then we’d need to improve that sensitivity by a factor of 10^37. 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 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 one 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 mass and distance between the masses 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 that same precision. Well, technically, half that precision because there are two masses. But the precision with which we can measure those mass positions is limited by the Heisenberg uncertainty principle, which 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 by the mass itself and we get the change in momentum due to the passage of one graviton.

Now we have an estimate for the uncertainty in the position needed to detect the graviton–remember it’s 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

So … 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 never be 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 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 actually 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.