Why does physics break down at the Planck scale?

At all times and locations, the laws of physics endure.

At the start of the hot Big Bang, the Universe was rapidly expanding and filled with high-energy, very densely packed, ultra-relativistic quanta. An early stage of radiation domination gave way to several later stages where radiation was sub-dominant, but never went away completely, while matter then clumped into gas clouds, stars, star clusters, galaxies, and even richer structures over time, all while the Universe continues expanding. The laws of physics, as known, apply at all times and locations to this picture.

Our Universe contains the Standard Model particles, plus whatever dark matter and dark energy are.

This diagram displays the structure of the Standard Model (in a way that displays the key relationships and patterns more completely, and less misleadingly, than in the more familiar image based on a 4×4 square of particles). In particular, this diagram depicts all of the particles in the Standard Model (including their letter names, masses, spins, handedness, charges, and interactions with the gauge bosons: i.e., with the strong and electroweak forces). It also depicts the role of the Higgs boson, and the structure of electroweak symmetry breaking, indicating how the Higgs vacuum expectation value breaks electroweak symmetry and how the properties of the remaining particles change as a consequence. Neutrino masses remain unexplained.

They interact via the four fundamental forces: gravity, electromagnetism, plus the two nuclear forces.

The idea of unification holds that all three of the Standard Model forces, and perhaps even gravity at higher energies, are unified together in a single framework. This idea, although it remains popular and mathematically compelling, does not have any direct evidence in support of its relevance to reality. Only electroweak unification, among all the unified possibilities, has been established.

Extensions potentially exist: grand unification, string theory, supersymmetry, a “fifth force,” etc.

The Standard Model particles and their supersymmetric counterparts. Slightly under 50% of these particles have been discovered, and just over 50% have never shown a trace that they exist. Supersymmetry is an idea that hopes to improve on the Standard Model, but it has yet to achieve the all-important step for supplanting the prevailing scientific theory: having its new predictions borne out by experiment.

However, there’s a scale where everything breaks down: the Planck scale.

The objects we’ve interacted with in the Universe range from very large, cosmic scales down to about 10^-19 meters, with the newest record set by the LHC. There’s a long, long way down (in size) and up (in energy) to the scales that the hot Big Bang achieves, which is only about a factor of ~1000 lower than the Planck energy. If the Standard Model particles are composite in nature, higher energy probes may reveal that, but ‘fundamental’ must be the consensus position today.

At sufficiently high energies, short distances, or brief timescales, making physical predictions becomes impossible.

Although we now know that light, as well as all quanta, can be described as both a wave and a particle under specific physical circumstances, there is a limit to how small a wavelength (or any length scale-dependent property) can be and still make physical sense: the Planck scale, or around ~10^-35 meters.

These limits are set by three fundamental constants: c, G, and ħ.

Light is nothing more than an electromagnetic wave, with in-phase oscillating electric and magnetic fields perpendicular to the direction of light’s propagation. The shorter the wavelength, the more energetic the photon, but the more susceptible it is to changes in the speed of light through a medium.

Combining the speed of light, gravitational constant, and reduced Planck constant creates Planck units.

Max Planck is often credited as the founder of quantum physics, as his early recognition that light, as well as matter, is quantized into discrete packets of energy, is one of the key tenets of our modern understanding of reality on a fundamental level. There are many quantum properties that bear his name, such as Planck’s constant (h) and the reduced Planck’s constant (ħ) found so frequently in quantum physics equations.

The Planck length is ~10^-35 m: √(ħG/c³).

The size, wavelength, and temperature/energy scales that correspond to various parts of the electromagnetic spectrum. You have to go to higher energies, and shorter wavelengths, to probe the smallest scales. On the smallest/shortest imaginable scales, down at lengths of around ~10^-35 meters, the laws of physics no longer make sense.

The Planck energy is ~10¹⁹ GeV: √(ħc⁵/G).

Cosmic rays, which are ultra-high energy particles originating from all over the Universe, including particles emanating from the Sun, strike atomic nuclei everywhere they exist. On Earth, they land in the upper atmosphere and produce showers of new particles, but even these particles cap out at around ~10^12 GeV, or a factor of several million below the Planck energy.

And the Planck time is ~10^-43 s: √(ħG/c⁵).

This diagram illustrates the inherent uncertainty relation between position and momentum, although a similar one exists for energy and time. When one is known more accurately, the other is inherently less able to be known accurately. Every time you accurately measure one, you ensure a greater uncertainty in the corresponding complementary quantity. On small enough timescales, known as the Planck time, a typical energy fluctuation will be great enough to trigger the creation of a black hole: a pathology in the theory.

A fundamental incompatibility between quantum physics and general relativity sets these limits.

Although, at a fundamental level, the Universe is made up of point-like quantum particles, they assemble together to create objects of finite sizes and masses, occupying specific amounts of volume. This artist’s illustration shows several electrons orbiting an atomic nucleus, where the electron is a fundamental particle, but the nucleus can be broken up into still smaller, more fundamental constituents. Whether there are structures on scales smaller than the presently known subatomic particles remains to be discovered.

In quantum physics, wave-like behavior is unavoidable.

The idea of a de Broglie wave is that every matter particle can also exhibit wavelike behavior, with the properties of the wave given by quantities like momentum and energy of the system. Everything, from electrons to human beings, behave like a wave under the proper conditions. The lower in momentum (i.e., the combination of velocity and mass) a particle is, the longer its de Broglie wavelength is.

All particles, with or without mass, possess inherent wavelengths.

Although visible light gives us a rich and varied view of objects in the Universe, it represents only a tiny fraction of the electromagnetic spectrum. The range from 0.4 to 0.7 microns, which is perceptible to human vision, is only a tiny blip compared to the full spectrum of wavelengths possible. However, there is a cutoff: waves cannot be detected on scales greater than the cosmic horizon, and do not exist (as far as we know) on scales smaller than the Planck length.

Shorter distances imply greater energies and shorter timescales.

Unlike the picture that Newton had of instantaneous forces along the line-of-sight connecting any two masses, Einstein conceived gravity as a warped spacetime fabric, where the individual particles moved through that curved space according to the predictions of general relativity. In Einstein’s picture, gravity is not instantaneous at all, but instead must propagate at a limited speed: the speed of gravity, which is identical to the speed of light. Unlike conventional waves, no medium at all is required for these waves to travel through.

But in general relativity, localized masses/energies have limits.

One of the most important contributions of Roger Penrose to black hole physics is the demonstration of how a realistic object in our Universe, such as a star (or any collection of matter), can form an event horizon and how all the matter bound to it will inevitably encounter the central singularity. Once an event horizon forms, the development of a central singularity is not only inevitable, it’s extremely rapid.

Exceed it, and an event horizon forms, creating a black hole.

In the vicinity of a black hole, space flows like either a moving walkway or a waterfall, depending on how you want to visualize it. At the event horizon, even if you ran (or swam) at the speed of light, there would be no overcoming the flow of spacetime, which drags you into the singularity at the center. Outside the event horizon, though, other forces (like electromagnetism) can frequently overcome the pull of gravity, causing even infalling matter to escape. Rotating black holes possess ring-like, not point-like, singularities.

But such black holes would instantly decay — via Hawking radiation — under the Planck time.

When a black hole either forms with a very low mass, or evaporates sufficiently so that only a small amount of mass remains, quantum effects arising from the curved spacetime near the event horizon will cause the black hole to rapidly decay via Hawking radiation. The lower the mass of the black hole, the more rapid the decay is, until the evaporation completes in one last “burst” of energetic radiation.

Successfully quantizing gravity, someday, should unveil the trans-Planckian regime.

It’s generally assumed that at some level, gravity will be quantum, just like the other forces. While the semi-classical approximation for computing the decay of black holes involves performing quantum calculations in the classical background of Einstein’s curved space, that approach might not be valid for describing the information encoded into the outgoing radiation. For this problem, like the trans-Planckian problem, gravity and quantum physics must be reckoned with together.

Mostly Mute Monday tells an astronomical story in images, visuals, and no more than 200 words.