Scientists have uncovered a hidden quantum limit that prevents an electron’s position and timing from ever being known with perfect precision.
Quantum physics sets hard limits on what can be known about a particle. Werner Heisenberg’s uncertainty principle famously states that position and momentum cannot both be measured with unlimited precision. The problem is not imperfect equipment. The restriction is built into nature itself.
Position and time were not thought to be governed by an equivalent rule. Now, researchers say they have uncovered a closely related boundary that appears when scientists try to track an electron across both space and time with extreme precision.
Teams at the Regensburg Center for Ultrafast Nanoscopy (RUN), led by Professors Jascha Repp, Rupert Huber, Franz Giessibl, and Klaus Richter, worked with researchers at the Max Planck Institute in Hamburg led by Angel Rubio. Together, they observed what they call a “space-time limit” for electron motion.
The finding reveals a fundamental tradeoff. The more precisely researchers determine when an electron moves, the less tightly its quantum wave packet can remain confined in space.
Why Watching Electrons Matters
Many future technologies depend on controlling electrons at scales far beyond the reach of conventional electronics. Faster computer chips, quantum information systems, advanced energy materials, and precisely directed chemical reactions all require a clearer picture of how electrons behave over extremely short distances and times.
Ordinary microscopes can capture detailed images of matter, but even the sharpest still image cannot reveal how an electron changes from one instant to the next. Researchers instead need something closer to an ultrafast movie, with each frame separated by attoseconds.
An attosecond is one billionth of a billionth of a second. On that scale, electrons can cross atomic distances and respond to light before atoms have time to noticeably move. Capturing such behavior is somewhat like filming a bullet while the surrounding landscape appears completely frozen, except the difference in speed is vastly greater.
Researchers at RUN previously used ultrafast scanning tunneling microscopy to follow the movement of a single molecule. Electrons posed a much harder challenge because they move roughly a thousand times faster than atoms and molecules on these scales.
Capturing Electrons in Attoseconds
To observe them, the team built a new laser system capable of generating precisely timed light pulses. The pulses controlled electrons moving between an atomically sharp metal tip and a silver surface separated by only a few atomic diameters.
The electron motion produced a measurable current. By changing the delay between two light pulses, the researchers reconstructed when the transfer occurred.
“By varying the time interval between the two laser pulses, we can directly observe how the electrons respond,” said lead author Simon Maier.
The experiment did not reveal electrons behaving like tiny balls traveling along predictable paths. Instead, they acted as quantum mechanical waves.
Filming Quantum Tunneling
The electrons crossed the gap through quantum tunneling, a process that allows particles to pass through an energy barrier they could not overcome under the rules of classical physics. Tunneling already plays an important role in modern technology, including scanning tunneling microscopes, semiconductor devices, and some forms of data storage.
In this experiment, the team could determine when tunneling occurred with attosecond precision.
“Our measurement can be understood as a high-speed camera for the electron wave packets, since you can see at what point in time the tunneling process takes place,” said doctoral researcher and co-author Katharina Glöckl.
Quantum simulations carried out by Angel Rubio’s group closely reproduced the experimental results. They also revealed that the electrons did not respond to the laser field instantly. Instead, their motion lagged behind by about 500 attoseconds.
Revealing the Space-Time Tradeoff
The experiment also exposed the limits of familiar descriptions of light. At these scales, the laser pulses could not be understood purely as waves or purely as streams of photons. Their behavior contained elements of both pictures, reflecting the dual nature of light in quantum physics.
That combination helped the researchers push deeply into the newly observed “space-time limit.”
The central tradeoff emerged when the team tried to pinpoint the timing of the electron transfer more precisely. Doing so required delivering more energy. That extra energy caused the electron’s wave packet to spread farther across space.
“The more precisely we want to pin down the electron’s position in time, the more energy we need to provide. And as a result, the electron wave packet spreads out more spatially,” explained co-author Raffael Spachtholz.
Measuring the Space-Time Tradeoff
To measure this relationship directly, the researchers placed a single atom on the surface. The atom acted as a tiny spatial constraint, briefly localizing the electron wave packet before the laser pulses arrived.
This allowed the team to compare how tightly the electron was confined in space with how precisely its movement could be measured in time.
Despite the intense laser excitation, the wave packets remained localized enough for atomic-scale imaging. That means researchers may be able to study ultrafast electron motion without losing the spatial detail needed to distinguish individual atoms.
The work turns a previously uncertain theoretical boundary into something that can be explored experimentally. Scientists can now investigate how the timing of electron motion changes the shape and spread of an electron’s wave function.
What This Means for Future Technology
The potential consequences extend beyond basic physics. For example, moving a single electron onto a molecule represents the smallest possible transfer of electric charge. If that transfer is compressed into an extremely small region of space and time, it can produce local peak current densities of up to 1 trillion amperes per square centimeter.
Such highly concentrated electron pulses could eventually give researchers a new way to initiate and control chemical reactions. Instead of heating an entire material or exposing it to prolonged radiation, scientists might direct energy toward a specific bond at a precisely chosen moment.
“In the future, we want to use such wave packets to specifically trigger chemical reactions and observe, on the relevant length and time scales, how chemical bonds can be broken or altered,” said Professor Jascha Repp.
“In the long term, the insights gained could also contribute to operating electronics and quantum information processing at the intrinsic speed limit of electron motion itself—hundreds of thousands of times faster than the currently dominant CMOS technology,” adds Prof. Rupert Huber.
Reference: “Tracking electrons at the space-time limit” by S. Maier, R. Spachtholz, K. Glöckl, C. M. Bustamante, S. Lingl, M. Maczejka, J. Schön, A. Riedel, K. Richter, F. J. Giessibl, F. P. Bonafé, M. A. Huber, A. Rubio, J. Repp and R. Huber, 3 July 2026, Nature Photonics.
DOI: 10.1038/s41566-026-01932-0
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