17

Gravitons and the nature of gravity

The marriage of quantum mechanics and general relativity will lead to quantum gravity (we hope)

Thus far, our discussion of gravity has been based entirely on classical physics. Even Hawking radiation is, strictly speaking, based on a classical understanding of gravity.

Some readers may be confused by this important point, since, in our telling of the Hawking story, we kept talking about quantum fluctuations producing particles and antiparticles. But note that these are quantum fluctuations in the field responsible for the particles and antiparticles (for example, the electron field), not quantum fluctuations in the gravitational field. Gravity’s job, so to speak, is “merely” to curve spacetime, and classical gravity is perfectly up to the task. The subject relevant to Hawking radiation is known as quantum field theory in curved spacetime.

In contrast, in a true quantum theory of gravity, space-time would be not only curved but also fluctuating like crazy. The gravitational field—namely, curved spacetime in Einstein’s theory—would itself be quantized.

Thus, to “complete” our understanding of physics as we now know it, we are obliged to marry quantum mechanics and general relativity. The result that physicists have longed for would be a theory of quantum gravity, in which curved spacetime is constantly fluctuating. There—you now have a hint why a complete theory of quantum gravity is so devilishly elusive: we simply can’t make sense of wildly fluctuating time and space, whatever that means.1

Enter the graviton

Let us now go back to gravity waves, but first, we review the more familiar case of electromagnetic waves. In classical physics, a light wave is simply a wave of electromagnetic energy. In quantum physics, however, energy comes in packaged units. When we examine a light wave more closely, we see that the wave actually consists of a huge number of tiny packets of electromagnetic energy called photons (as was already mentioned in chapter 3.) The photon² is the fundamental particle of light.

The situation reminds me of those nature films with aerial shots of migrating herds of wildebeests. From a distance, we see a dark brown tide surging forward. As the lens zooms in, we see the tide differentiating into individual wildebeests thundering along. Similarly, as we zoom in and examine Nature more closely, we see what classical physicists took to be a wave of light differentiating into individual photons cruising along.³

In the same way, at the quantum level, a gravity wave consists of packets of gravitational energy called, appropriately enough, gravitons.*

A swarm of gravitons

Classical physicists speak of massive objects responding to the gravitational fields generated by one another. To a quantum physicist, the gravitational field consists of a swarm of gravitons. A massive object generating a gravitational field is actually emitting and absorbing these teensy-teensy bits of gravitational energy. Thus, in quantum physics, two massive objects interact gravitationally by exchanging gravitons. Similarly, two electric charges interact by exchanging photons.

You could say that we are literally swimming in a swarm of gravitons generated by the earth.

Ceaseless begetting leads to no end of trouble

I promised, way back in chapter 3, to tell you about a huge difference between gravity and electromagnetism, a difference that causes theoretical physicists no end of trouble. The seed for this difference is already sown by Einstein’s theory of special relativity, which states that mass and energy are the same.

Consider a massive object, such as a star. The mass generates a gravitational field around it, according to Newton and Faraday. But a field contains energy. That’s fine by Newton and Faraday. But no, Einstein said that energy is the same as mass. Therefore, if mass could generate a gravitational field, then so can energy. The energy in the gravitational field in turn generates a gravitational field.

A gravitational field begets another gravitational field. The process continues with no end in sight: a process described mathematically as an infinite series. It is this ceaseless begetting that could cause spacetime to literally curl up on itself,^*forming a black hole, for example.

Contrast the gravitational field with the electric field. An electric charge generates a electric field. The electric field carries energy, but not charge. It does not generate another electric field. The process ends. An electric field does not beget another electric field.*

As mentioned earlier, electromagnetism is said to be linear in physics jargon, and hence, in some sense, is considered “trivial.” In contrast, gravity is highly nonlinear and a terror to deal with. For example, using traditional mathematics (by this I mean “analytic methods” in the jargon, that is, using pencil and paper), we would have no hope of computing the gravitational wave generated in the final throes of two black holes merging. Computers with enormous computing power were used to produce the theoretical curves⁴ to compare the detected signal with, as was actually needed for LIGO and was mentioned in chapter 9.

Note two important points. First, the ceaseless begetting already arises in classical Einstein gravity, even before we try to quantize gravity. Second, this difficulty with nonlinearity is technical, not conceptual. It reflects our inability to calculate using analytic methods.

Our quantum crank does not appear to work for gravity

Here I pause briefly to clarify a potential point of confusion for many readers, who might have read that physicists often speak of quantizing this or that theory. Indeed, the word “quantize” used as an active verb means to change a classical theory into a quantum theory. Thus, when we quantize Newton’s classical mechanics, we obtain quantum mechanics, and when we quantize Maxwell’s classical electrodynamics, we obtain quantum electrodynamics, and so on and so forth. By now, quantization consists of a procedure taught to students: it is a crank that physicists turn to change any classical theory into a quantum theory.

But there is no guarantee that the resulting quantum theory will make sense, or more technically, will behave “nicely.” When we put Einstein gravity under the quantum crank and turn it, we produce a wild man of a theory. More precisely, in processes involving gravity, quantum fluctuations grow with energy, so that when we reach the so-called Planck energy, about 10¹⁹ GeV, the fluctuations get to be so big that they go totally out of control.5 That the trusted quantum crank does not work for gravity has been of course the Mother of all headaches for theoretical physics for the past eight decades or so.

Readers with a long memory will recall that I introduced, way back in chapter 2, the humongous Planck number 10¹⁹ as a measure of how feeble gravity is. Yes, the Planck energy* is simply related to the Planck number, and again reflects how “out of place” gravity is compared to the other three interactions.

By the way, after the detection of gravitational waves, some in the popular press thought that the discovery would help us understand quantum gravity. But this is a bit of a misunderstanding. The gravitational wave that came to us from 1.3 billion light years away is totally a classical wave. LIGO certainly did not detect individual gravitons.

The ceaseless begetting we just talked about is at least partly responsible for this giant headache, but there are other theories⁶ with ceaseless begetting that we have mastered. A more serious problem might be our inadequate understanding of spacetime.

It may be helpful to recall the history leading from the discovery of electromagnetic waves in 1886 to an understanding of quantum electrodynamics. Theoretical understanding cannot be dated precisely: it is not as if theoretical physicists did not understand quantum electrodynamics one day and woke up the next morning with a complete understanding. But for the sake of the discussion, let us pick 1950, 64 years after the detection of electromagnetic waves. By this naive “reasoning,” we might expect quantum gravidynamics7 in 2080. The analogy is clearly too miserable to be trusted at all, since quantum mechanics, finally formulated in its present form in 1926, was not even a dream in 1886.

The standard view about the struggle to master quantum gravity is that we have the correct crank; we are just not turning it correctly.

I would suggest an alternative possibility: a new structure will have to appear in physics before we can master quantum gravity. Some might say that the structure has already arrived in the guise of string theory, but it may be far more exciting for theoretical physics to enter into a truly revolutionary framework comparable in depth to quantum mechanics. Perhaps quantum mechanics will have to be modified or extended. Pushing our silly “analogy” further than it can bear, we might expect this around 2056, 40 (=1926 — 1886) years after the detection of gravitational waves.

The quantum dance of two massive objects

Consider two massive objects, say, you and the earth. The gravitons emitted by one massive object are absorbed by the other, and vice versa, as was noted earlier.

This is how quantum physicists picture the gravitational boogie-woogie between two massive objects: as they move and shake it all about, they exchange gravitons. By the way, if you have heard of Feynman diagrams and wondered what they were, an example would be a diagram depicting the process just described in English.8 The process repeats itself rapidly. This constant exchange of gravitons between the two objects produces the observed gravitational force. (Similarly, the constant exchange of photons between two charged particles produces the observed electromagnetic force.)

A Feynman diagram describing the exchange of a graviton (the wavy line) between two particles (the solid lines with arrows on them). You may think of this as a process occurring in spacetime, with time along the vertical axis, and space along the horizontal axis.

I have likened this constant exchange of gravitons to the marriage brokers of old traveling between two parties, telling each the other’s intentions.⁹

Since the early days of physics, the notion of force has been among the most basic and the most mysterious. It was thus with considerable satisfaction that physicists finally understood the origin of force as being due to the quantum exchange of mediator particles, such as the graviton and the photon.

A moral imperative but not a practical necessity

Some readers may be justifiably confused at this point.

“You told us earlier that, through the decades, physicists have failed to construct a well-behaved theory of quantum gravity, but now you say that the everyday phenomenon of gravity can be understood as due to the exchange of gravitons. What is going on?”

In everyday gravity, for example, that almost but not quite fatal attraction between you and the earth, the gravitons emitted by the earth play nice: each graviton gets to you without messing around with the other gravitons. Similarly, the gravitons emitted by you get to the earth directly. In more technical language, the gravitons being exchanged between you and the earth go directly from one massive body to the other, without pausing to interact with other gravitons. The gravitons are said to propagate freely. It is when the gravitons party with each other that all hell breaks loose, so to speak, and quantum gravity as we know it goes totally haywire.

In this context, we are saved by the absurd weakness of gravity that we talked about in chapter 2. As was explained, the interaction of the gravitational field with matter is extremely weak. The effect of the gravitons propagating between you and the earth interacting with each other produces only a tiny correction to Newton’s law of gravity.

Thus, as you would suspect, Newton’s classical gravity suffices for almost all practical purposes, from building skyscrapers to putting up satellites. The desperate search for quantum gravity is not a practical necessity, but a “moral imperative.” Indeed, while some seekers after quantum gravity are ready to kill themselves over this massive failure of will, or at least to gnash their teeth and look grim, other physicists are not in the least bothered by the failure to quantize gravity.¹⁰

*  Physicists have only recently detected gravity waves, so they have certainly not seen a graviton. Indeed, to the extent that the future is foreseeable, experimentalists see no prospect of ever detecting individual gravitons. Nevertheless, as much as they believe in quantum physics, theorists believe in the graviton.

*  Not so different from the water wave at the beach curling up on itself, as mentioned in chapter 4.

*  This statement is true in classical physics. In the quantum world, an electric field can generate another electric field, but under normal circumstances, the effect is weak.

*  As another way to appreciate how huge the Planck energy is, note that the Large Hadron Collider (LHC), the world’s most powerful accelerator, can reach an energy of about 10⁴ GeV.