Cobra Effect · Famous myths
Is the Planck length the smallest possible length?
Where the smallest length came from, and what has actually been measured.
7 cards, read aloud in 4:15, with a test and sources.
Zoom in far enough, people say, and space turns into pixels.
The story goes that nothing can be shorter than one tiny distance, called the Planck length. It is about a hundred billion billion times smaller than a proton. Below it, you will often read, space comes in tiny blocks, like the dots that make up a printed picture. It is a lovely idea. Nobody has shown that it is true.
The length comes from Max Planck, and in 1899 he was only making units.
He combined constants of nature, among them the strength of gravity, the speed of light, and a constant from his own work on the glow of hot objects. Multiplied and divided the right way, they give a length, a mass, a time and a temperature. Such units, he wrote, would keep their meaning for all times and all civilisations, even ones that are not human. He said nothing about a smallest anything.
The idea of a limit came later, from a thought experiment.
To see something small you need light of a short wavelength, and shorter wavelengths carry more energy. In 1936 the Soviet physicist Matvei Bronstein noticed the catch. Energy has gravity, and too much of it packed into too small a space collapses under its own pull. In 1964 Alden Mead argued that this stops any measurement finer than about the Planck length. The probe would hide the very thing it was sent to look at. It is a strong hint. It also stretches two theories far beyond where either has been tested.
Nothing has ever been measured anywhere near it.
The most powerful collider ever built probes distances far smaller than a proton. The Planck length is still about a million billion times smaller than that. By one estimate, reaching it directly would take a particle accelerator the size of a galaxy. So every claim about what happens down there is theory, not measurement.
The leading theories disagree, and none of them describes a grid.
One approach, from Carlo Rovelli and Lee Smolin in 1995, says areas and volumes come in steps, a little like the energy levels of an atom. Another, from 1987, builds space and time out of points scattered at random, joined only by what comes before what. String theory keeps space smooth, though its strings blur anything much smaller than themselves. None of the three has been confirmed by experiment. A regular grid is the one picture most physicists have set aside. Someone flying past would see it squashed, and no experiment has found space treating one motion as special.
In May 2009 a space telescope watched a race between two kinds of light.
Some ideas about grainy space predicted that high energy light would travel very slightly slower than low energy light. NASA’s Fermi telescope caught a burst of gamma rays that had been travelling for about seven billion years. The most energetic light arrived within a second of the least. That ruled out the simplest version of the slowing, right up to the Planck scale. In 2024 an observatory in China pushed the limit about ten times further. It did not show that space is smooth. Subtler kinds of graininess would pass the same test.
So when you hear that the universe has a smallest size, ask who measured it.
Nobody has. The Planck length is the scale where gravity and quantum theory can no longer ignore each other. Almost every physicist expects something new to happen near it. What that is, nobody knows. It may be a smallest length. It may be that length itself stops meaning anything. A number worked out on paper is a signpost. It is not a discovery.
Sources
- The Planck Length, John Baez, University of California, Riverside. A short, honest account of why this length is where quantum blur meets the size of a black hole, with the loopholes in the argument spelled out.
- Fermi Telescope Caps First Year With Glimpse of Space-Time, NASA. The 2009 gamma ray burst race in plain language, and what the result meant for ideas of grainy space.
- Testing Einstein’s special relativity with Fermi’s short hard gamma-ray burst GRB090510, Fermi GBM and LAT Collaborations, 2009. The free version of the Nature paper. The authors say plainly that only the simplest kind of energy dependence is ruled out.
- Quantum Gravity, Steven Weinstein and Dean Rickles, Stanford Encyclopedia of Philosophy. What the rival theories say about space at the smallest scales, and the plain statement that there are no experiments yet.
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