Physics & Quantum Science

Beyond Heisenberg: The New Space-Time Limit That Governs Every Electron

Heisenberg's uncertainty principle says you cannot know both a particle's position and momentum with perfect precision. Now researchers have discovered a closely related boundary — a "space-time limit" — that governs how precisely an electron's position and timing can be known at the same time.

• Using ultrafast scanning tunneling microscopy with attosecond laser pulses, researchers at the University of Regensburg tracked individual electrons as they tunnelled across a gap only a few atomic diameters wide — the first time anyone has reached the quantum mechanical space-time limit for electron motion.
• The newly observed tradeoff works like this: the more precisely you determine when an electron moves, the less tightly its quantum wave packet can remain confined in space. This is analogous to Heisenberg's principle but for space and time rather than position and momentum.
• Published in Nature Photonics, the work involved teams from the Regensburg Center for Ultrafast Nanoscopy (RUN) and the Max Planck Institute in Hamburg. The findings have direct implications for future quantum computers, ultrafast electronics, and the control of chemical reactions at the atomic scale.

Quantum physics sets hard limits on what can be known about a particle. Werner Heisenberg's uncertainty principle, formulated in 1927, famously states that position and momentum cannot both be measured with unlimited precision — not because of imperfect equipment, but because the restriction is built into nature itself. Until now, position and time were not thought to be governed by an equivalent rule.

Researchers at the Regensburg Center for Ultrafast Nanoscopy (RUN), led by Professors Jascha Repp, Rupert Huber, Franz Giessibl, and Klaus Richter, together with theorists at the Max Planck Institute in Hamburg led by Angel Rubio, have now closed that gap. They observed what they call a "space-time limit" for electron motion, revealing a fundamental tradeoff: the more precisely scientists determine when an electron moves, the less tightly its quantum wave packet can remain confined in space.

The team built a new laser system capable of generating precisely timed light pulses that controlled electrons moving between an atomically sharp metal tip and a silver surface. The electrons crossed the gap through quantum tunnelling, a process that allows particles to pass through energy barriers they could not overcome under classical physics. By varying the delay between two laser pulses, the researchers reconstructed exactly when the electron transfer occurred — with attosecond precision. An attosecond is one billionth of a billionth of a second, a timescale on which electrons can cross atomic distances before atoms have time to noticeably move.

"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 travelling along predictable paths. Instead, they acted as quantum mechanical waves, their behaviour reflecting the dual nature of light and matter at the smallest scales.

The space-time limit has important implications for future technologies. 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. Many future technologies depend on controlling electrons at scales far beyond the reach of conventional electronics, and this discovery sets a fundamental boundary for what is possible — a boundary that engineers will need to work within, just as they already work within Heisenberg's original uncertainty principle.