## From Ethan Siegel: “This Simple Thought Experiment Shows Why We Need Quantum Gravity”

From Ethan Siegel

Jul 27, 2018

Quantum gravity tries to combine Einstein’s general theory of relativity with quantum mechanics. Quantum corrections to classical gravity are visualized as loop diagrams, as the one shown here in white. Whether space (or time) itself is discrete or continuous is not yet decided, as is the question of whether gravity is quantized at all. (SLAC NATIONAL ACCELERATOR LAB)

**If our current laws of physics can’t predict what will happen, even probabilistically, we need something new.**

There are two theories we have that explain all the particles and their interactions in the known Universe: General Relativity and the Standard Model of particle physics. General Relativity describes gravity perfectly everywhere we’ve ever looked. From the smallest-scale attractions we’ve ever measured in a laboratory to the expansion and curvature of space due to Earth, the Sun, black holes, galaxies, or the entire Universe, our observations and measurements have never deviated from what we’ve observed. The Standard Model is equally successful for the other three forces: electromagnetism and the strong and weak nuclear forces. Every experiment, measurement, and observation has agreed perfectly with these two theories.

It sounds great, until you try to combine the two. If we do that, it all falls apart. The solution? We need a quantum theory of gravity. Here’s why.

The spacetime curvature around any massive object is determined by the combination of mass and distance from the center-of-mass. Other concerns, like velocity, acceleration, and other sources of energy, must be factored in. (T. PYLE/CALTECH/MIT/LIGO LAB)

From Einstein’s theory of gravity, we can compute what the curvature of space is at any location in the Universe, from here on planet Earth to the largest scales in the cosmos. We’ve performed experiments that have tested the gravitational force law down to micron-sized scales, and on astrophysical scales in extreme environments, such as the galactic center, merging neutron stars, and at the edges of black holes. Even esoteric predictions, such as the production of gravitational waves, the effect of frame-dragging, or the precession of planetary orbits, are completely in line with every measurement we’ve ever taken. In every case, Einstein’s theory perfectly describes reality.

The Standard Model of particle physics accounts for three of the four forces (excepting gravity), the full suite of discovered particles, and all of their interactions. Quarks and leptons are fermions, which have a host of unique properties that the other (bosons) particles do not possess. (CONTEMPORARY PHYSICS EDUCATION PROJECT / DOE / NSF / LBNL)

From the Standard Model, we know how electricity, magnetism, radioactive decays and nuclear forces work. Take any particle and let it interact (or not) with anything else in the Universe, and we’ll know the probability distribution of all possible outcomes. Even though the quantum world isn’t entirely deterministic, we can still successfully describe the expected set of outcomes in a mathematically precise fashion. If we perform the same experiment thousands upon thousands of times, we’ll see the results match our best quantum predictions, even for bizarre and unintuitive setups.

But if we take a look at one such setup in particular — the famed double-slit experiment — we can see immediately why a quantum theory of gravity is absolutely necessary.

The wave-like properties of light became even better understood thanks to Thomas Young’s two-slit experiments, where constructive and destructive interference showed themselves dramatically. These experiments were known for classical waves since the 17th century; around 1800, Young showed they applied to light as well. (THOMAS YOUNG, 1801)

Imagine you’ve got a set of quantum particles: they could be photons, neutrinos, electrons, or anything else. Imagine that you’ve set them up so they’ll bombard a tiny area of a barrier, with two slits cut into the barrier extremely close together, to allow these quantum particles to pass through. Behind the barrier, you’ll set up a screen, so you can detect where the particles wind up. This is the classic setup of the double slit experiment.

If you send through a bunch of particles at once, they act just like a wave. The particles might go through one slit or the other, but they interfere. At the end of the day, you wind up with a clearly identifiable interference pattern on the screen, the same way you would for a water wave passing through a similar set of slits.

Double slit experiments performed with light produce interference patterns, as they do for any wave. The properties of different light colors is due to their differing wavelengths. (TECHNICAL SERVICES GROUP (TSG) AT MIT’S DEPARTMENT OF PHYSICS)

Well, you can’t have your particles interfering with one another, so you decide to send them through one-at-a-time. You measure where it hits the screen and record it, and then you fire the next particle. It doesn’t matter which particle you choose; if we can detect it on the screen, we see the same behavior. The interference pattern builds up one-particle-at-a-time, but clearly emerges. Somehow, these quantum particles are passing through both slits simultaneously, and are interfering with themselves.

The wave pattern for electrons passing through a double slit, one-at-a-time. If you measure “which slit” the electron goes through, you destroy the quantum interference pattern shown here. Note that more than one electron is required to reveal the interference pattern. (DR. TONOMURA AND BELSAZAR OF WIKIMEDIA COMMONS)

Perhaps you decide you’re not a fan of this quantum weirdness, so you decide to measure which slit each particle goes through. You set up a photodetector around each slit, and measure when a particle passes through it. The first particle goes through, and you detect its passage through slit #2. The second one arrives, and also goes through slit #2. The third one goes through slit #1, then the fourth through #2, and then the fifth through #1 again. You repeat this, over and over, for thousands of particles. And when you look at the resulting pattern on the screen, you find something extremely troublesome: the interference pattern is gone. Instead, all you see is a pile of particles that passed through slit #1, along with another pile that passed through slit #2. They did not interfere.

If you measure which slit an electron goes through, you don’t get an interference pattern on the screen behind it. Instead, the electrons behave not as waves, but as classical particles. (WIKIMEDIA COMMONS USER INDUCTIVELOAD)

This is weird! This unintuitive weirdness is at the heart of what makes quantum physics, and the Standard Model in general, such a powerful tool. At a fundamental, quantum level, we can accurately predict when you have this quantum behavior and when you won’t, and what that behavior will look like when it appears.

For the electromagnetic, strong nuclear, and weak nuclear forces, this works exquisitely well. It works so well that, as bizarre as they may be, no repeatable experiment has ever disagreed with any significance from the Standard Model’s predictions. And yet, if we were to ask the following simple question, we don’t have any way to arrive at an answer:

What happens to the gravitational field of an electron when it passes through a double slit?

The gravitational field of the electron, as it passes through a double slit, would behave differently if gravity is fundamentally quantum (bottom) or non-quantum (top). (Sabine Hossenfelder)

The reason we can’t answer it is we don’t know a huge number of properties about gravity on the quantum scale. We don’t know whether gravity is quantized or not. The particles must be quantized, but gravity might not be, and if it isn’t, the double slit experiment would give different results than if it is.

We don’t know whether space is fundamentally discrete (with a minimum length scale) or continuous. If there were a minimum length, there would be a fundamental resolution limit to our experiments, one we might someday encounter at high enough energies. There are questions we cannot answer about how gravity behaves under certain experimental conditions.

Even two merging black holes, one of the strongest sources of a gravitational signal in the Universe, doesn’t leave an observable signature that could probe quantum gravity. For that, we’ll have to create experiments that probe either the strong-field regime of relativity, i.e., near the singularity, or that take advantage of clever laboratory setups. (SXS, THE SIMULATING EXTREME SPACETIMES (SXS) PROJECT (BLACK-HOLES.ORG))

We know, in principle, that the gravitational field should remain localized around the electron’s position, just as it would for any mass. But what does this mean when the electron’s position is inherently uncertain? Does the gravitational field always go primarily through one slit or the other? And does the act of observing (or not observing) change the gravitational field? And if so, how?

The gravitational field of the electron is weak; we cannot observe it in practice. Equations developed by Wheeler, Feynman, and DeWitt in the 1960s describe the expected behavior of a particle in the weak-field limit of quantum gravity, but those equations have never been experimentally tested. To do so is presently beyond the realm of what we’re capable of, but there is hope.

The experimental setup that’s enabled the measurement of gravitational fields and effects down to milligram-scale masses, From “A micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses.”

There are proposed experimental setups that would allow us to measure the gravitational field more precisely than ever before: down to milligram masses. On the other hand, we’ve managed to bring relatively large objects (compared to fundamental particles) into quantum superpositions of states: up to nanogram-scale masses. The exact energy levels of these states depend on the total gravitational self-energy of the system, making this a realistic, plausible test to determine whether gravity is quantized or not. When technology and experimental techniques advance far enough, these two scales will intersect. When that moment comes, we’ll be able to probe the quantum gravitational regime.

The energy levels of a nanogram-scale disk of osmium, and how the effect of self-gravitation will (right) or won’t (left) affect the specific values of those energy levels. The disk’s wavefunction, and how it’s affected by gravitation, may lead to the first experimental test of whether gravity is truly a quantum force. (ANDRÉ GROSSARDT ET AL. (2015); ARXIV:1510.0169)

The description that General Relativity puts forth — that of matter telling space how to curve, and curved space telling matter how to move — needs to be augmented to include an uncertain position that has a probability distribution to it. Whether gravity is quantized or not is still an unknown, and has everything to do with the outcome of such a hypothetical experiment. How an uncertain position translates into a gravitational field, exactly, remains an unsolved problem on the road to a full quantum theory of gravity. The principles that underlie quantum mechanics must be universal, but how those principles apply to gravity, and in particular to a particle passing through a double slit, is a great unknown of our time.

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“Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible,” says Ethan

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