A hundred years ago this week, at the height of the quantum revolution, Austrian physicist Erwin Schrödinger submitted a manuscript for publication. Its centerpiece was an innocuous-looking equation that would alter science’s entire conception of reality.
Even now the Schrödinger equation remains physicists’ foremost window into the quantum realm. It tells scientists how that strange world works; that is, how quantum objects interact with their surroundings. But in doing so, it sets the mysteries of quantum mechanics—many of which elude understanding to this day—in stark mathematical relief.
A full century after Schrödinger penned his famous equation, scientists and philosophers are still seeking to define—and expand—its hazy boundaries. It does a great job describing the quantum systems that physicists study in their labs. But should the physicists themselves really be left out of the equation?
As nonsensical as this question may seem, attempts to answer it are already offering new and surprising lessons about the quantum world. Inserting the observer into the Schrödinger equation, it seems, allows transformative new perspectives on century-old questions.
“We’ve been trying to do physics as though it’s just there,” says Anne-Catherine de la Hamette, a physicist at the Swiss Federal Institute of Technology Zurich. “And we forgot to ask, ‘Well, who is actually measuring stuff?’”
An Insider’s Perspective
Before Schrödinger’s 1926 breakthrough, the quantum revolution was in full swing but had mainly produced a hodgepodge of confounding truths. A particle could apparently be located in two places at once. Solid objects would sometimes act like ethereal waves of probability. Measuring an electron’s spin on Earth could tell you instantaneously the spin of its entangled partner on Mars.
The Schrödinger equation gave physicists a handle on this weird world. It determines the wave function, a mathematical object—technically, a complex-valued function of probability amplitudes—that captures all of a quantum system’s myriad possibilities. If you have an electron’s wave function, you can calculate how likely you are to find it in one place versus another.
The equation says how the wave function evolves over time but only while the system is left unobserved. The moment you check on, say, the position of an electron, its wave function “collapses,” instantly snapping from a cloudlike distribution of possible places the particle might be to a narrow peak where it actually was. Experts still aren’t sure how the act of measuring disrupts the quantum system, but it’s unavoidable—the “measurement problem” remains the central mystery of quantum mechanics. The field of quantum reference frames, however, approaches it from a new direction.
“It’s really about describing a quantum system from the inside,” says Philipp Höhn, a physicist at the Okinawa Institute of Science and Technology in Japan.
Entangled Perspectives
To “observe” a quantum system requires a measurement device, like a clock. But even clocks, in theory, are governed by quantum mechanics. “Because the clock is quantum, it’s subject to the uncertainty principle,” says Joshua Kirklin, a physicist at the Perimeter Institute for Theoretical Physics in Ontario, referring to Werner Heisenberg’s realization in 1927 that certain properties of quantum systems can never be known with total certainty. “That means that the time that you measure is fuzzy.”
Quantum reference frames account for this. They update the wave function in the Schrödinger equation so that it describes both the system and the “clock” a scientist is using to measure it, complete with the fuzziness of that measurement.
And once devices like clocks are included in the quantum system, physicists are able to ask what two observers using different “quantum clocks” will then see.
This small change leads to surprising results. In 2019 physicists used it to show that the phenomenon of quantum entanglement isn’t an objective fact—it actually depends on the circumstances of the observer. “Things that don’t look entangled in one frame can look entangled in another,” de la Hamette says. The same is true for the phenomenon of superposition, where a quantum object is described by a combination of distinct possibilities at once.
Uncertain Spacetime
Einstein’s general theory of relativity, with its mind-bending revelations about the subjectivity of space and time, has long had issues meshing with quantum mechanics. Yet there are hints that quantum reference frames might offer a new approach here as well.
Take black holes. Their gravity warps space and time around them so much that no information from their confines can escape back out to the wider universe. But they also have a temperature and an entropy—emergent physical quantities that usually arise from the quantum mechanical depths. Reconciling these seemingly contradictory properties using the same math is one of modern physics’ great challenges.
But in a 2023 paper, a team of physicists, including the great theoretician Edward Witten, added an observer with a quantum clock to their treatment of a black hole and were surprised to find the gnarly math became simpler. Entropies that seemed infinite, impossible to calculate, suddenly became tractable. “If you take quantum reference frames into account, you find those infinities are made finite,” Kirklin says.
And, if this new perspective can help break the impasse over black holes, what other long-standing puzzles might it help physicists solve?
New Century, New Outlook
Invigorated by this success, quantum reference frame enthusiasts gathered last year at a conference in Okinawa, the first of its kind, to discuss what would come next. “It seems to be becoming a community,” Kirklin says. “It’s really accelerated recently.”
Much of the focus remains on quantum gravity. Relativity is all about relating different frames of reference, so making these “quantum” could be a path to resolving the many paradoxes that spring from Einstein’s theory. “Space and time, which normally we use as this background stage on which physics is happening, that itself becomes uncertain,” says de la Hamette. “How do we then describe anything?”
But physicists aren’t stopping there. They hope to pierce the quantum world’s deepest secrets. They’ve begun discussing “Wigner’s friend,” a thought experiment related to the measurement problem and its more famous cousin, Schrödinger’s cat. Perhaps this new lens on these old quandaries will continue to bring physicists closer to the biggest question of all: What happens to a quantum system at the moment of observation?
“The lesson may be,” de la Hamette says, “that we should not have forgotten the observer.”