1761: "At the Space-Time Limit"
Interesting Things with JC #1761: "At the Space-Time Limit"
In 2026, researchers measured an electron moving through a barrier in less than a femtosecond while still seeing where it was at the scale of a single atom. The experiment pushes electron observation into times measured in attoseconds without losing the atomic-scale view.
Curriculum - Episode Anchor
Episode Title: At the Space-Time Limit
Episode Number: 1761
Host: JC
Audience: Grades 9–12, introductory college, homeschool, lifelong learners
Subject Area: Physics, quantum mechanics, nanoscience, photonics, engineering, scientific literacy
Lesson Overview
Learning Objectives
Explain quantum tunneling and distinguish an electron wavefunction from a classical particle trajectory.
Compare femtosecond, attosecond, angstrom, and nanometer scales and connect them to electron dynamics.
Describe how lightwave-driven scanning tunneling microscopy combines ultrafast temporal resolution with atomic-scale spatial resolution.
Analyze why changes in an electron wave packet's temporal behavior can be connected to changes in its spatial distribution.
Essential Question: How can scientists observe electron dynamics on their natural time and length scales without losing atomic-scale spatial information?
Success Criteria
Students can accurately define quantum tunneling, wavefunction, femtosecond, attosecond, and angstrom.
Students can explain the purpose of the two delayed near-infrared pulses used in the experiment.
Students can distinguish the experiment's "space-time limit" from Heisenberg's position-momentum uncertainty principle.
Students can use evidence from the episode to explain why simultaneous spatial and temporal resolution matters.
Student Relevance Statement: Modern electronics, quantum technologies, materials science, and chemistry depend on understanding electron behavior at scales far smaller and faster than direct human perception.
Real-World Connection: Electron rearrangements occur during charge transfer, light-matter interactions, chemical processes, and the operation of nanoscale electronic systems.
Workforce Reality: Ultrafast microscopy connects physics with careers in semiconductor research, photonics, quantum technology, computational physics, materials science, nanotechnology, scientific instrumentation, and chemical research.
Key Vocabulary
Terms
Scanning tunneling microscope (STM)(SKAN-ing TUN-uhl-ing MY-kruh-skohp) — An instrument that uses quantum tunneling current between a sharp conducting tip and a surface to investigate matter at extremely small spatial scales.
Quantum tunneling(KWON-tum TUN-uhl-ing) — A quantum phenomenon in which a particle's wavefunction extends through an energy barrier that the particle could not classically cross with its available energy.
Wavefunction(WAYV-funk-shun) — A mathematical description of a quantum system from which probabilities and other physical information about the system can be determined.
Wave packet(WAYV PAK-it) — A spatially localized combination of waves used to represent a quantum particle such as an electron.
Femtosecond(FEM-toh-sek-und) — 10−1510^{-15} second, or one quadrillionth of a second.
Attosecond(AT-oh-sek-und) — 10−1810^{-18} second, one thousandth of a femtosecond.
Angstrom (Å)(ANG-strum) — 10−1010^{-10} meter, or one ten-billionth of a meter.
Photon-assisted tunneling(FOH-ton uh-SIS-tid TUN-uhl-ing) — Tunneling in which interaction with photons changes the electron's energy and influences the tunneling process.
Near-infrared (NIR)(NEER IN-fruh-red) — Electromagnetic radiation just beyond visible red light; controlled NIR pulses were used to drive electron dynamics in the experiment.
Narrative Core
Open: An electron tunneling across the tiny junction of a scanning tunneling microscope cannot simply be followed like a ball moving along a visible path. Quantum mechanics instead describes its behavior through a wavefunction, and the relevant changes can occur in less than a femtosecond.
Info: Researchers at the University of Regensburg and the Max Planck Institute for the Structure and Dynamics of Matter combined atomic-scale scanning tunneling microscopy with phase-controlled near-infrared light pulses. Their method identified isolated electron tunneling transients shorter than one femtosecond while investigating the spatial extent of the electron wave packet.
Details: Two time-delayed laser pulses modified the tunneling barrier and provided a way to trace electron response on attosecond timescales. Quantum simulations connected the measured tunneling current with the underlying wavefunction dynamics. The spatial extent depended on the interplay between multiphoton and field-driven behavior. Under optimized conditions, the researchers maintained angstrom-scale localization and demonstrated the technique by mapping a single copper adatom on a silver surface.
Reflection: The experiment illustrates a central challenge of ultrafast nanoscience: increasing temporal resolution is valuable only if the spatial information needed to distinguish atomic-scale behavior can also be preserved. The reported "space-time limit" concerns this coupling between temporal dynamics and the spatial structure of electronic wavefunctions; it is not a new form of Heisenberg's position-momentum uncertainty principle.
Closing: These are interesting things, with JC.
Episode cover for Interesting Things with JC #1761: At the Space-Time Limit. Large silver and orange title text appears over a dark, space-like background. Below, blue and orange waveforms converge at a bright point above a glowing, curved grid, visually suggesting ultrafast electron behavior across space and time.
Transcript
Interesting Things with JC #1761:
"At the Space-Time Limit"
An electron crossing the tiny gap inside a scanning tunneling microscope doesn't move along a path we can simply watch. Quantum mechanics describes it as a wavefunction, and when that electron tunnels through an energy barrier, the whole event can happen in less than a quadrillionth of a second. For a long time, that left researchers with a tradeoff: they could get an extraordinarily sharp look at where an electron was behaving, or an extraordinarily fast look at when it was behaving, but getting both at once was another problem.
In 2026, researchers at the University of Regensburg and the Max Planck Institute for the Structure and Dynamics of Matter pushed a scanning tunneling microscope into that gap. They combined atomic-scale microscopy with carefully controlled near-infrared laser pulses and measured tunneling events lasting less than one femtosecond. A femtosecond is one millionth of one billionth of a second. An attosecond is another thousand times shorter, and that's the range where parts of this experiment were operating.
The researchers describe what they were approaching as the electron's "space-time limit." That doesn't mean they've found a new version of Heisenberg's uncertainty principle. Heisenberg deals with limits on how precisely position and momentum can be known together. This is different. When an electron is driven on these extremely short timescales, the size and shape of its wavefunction can change too, so getting a faster look at the electron can affect the spatial picture you're trying to see.
To get around that, the team used two carefully delayed laser pulses to create controlled electric fields across the microscope's tunneling junction. Those fields changed the barrier the electrons had to cross. By adjusting the timing and strength of the light, the researchers could measure changes in the tunneling current in less than a femtosecond while also tracking how far the electron's wave packet spread through space. Quantum simulations helped them match what they measured to what the electrons were actually doing.
And the behavior wasn't as simple as making the electron move faster. Photon-assisted tunneling could delay the electron and spread its wavefunction farther through the junction, while changing the strength of the driving field changed how far that wavefunction spread. The team found conditions where the tunneling event stayed shorter than one femtosecond while the electron wave packet remained confined to only a few angstroms. An angstrom is one ten-billionth of a meter, or about four billionths of an inch.
Then they tried it on something you can actually name: one copper atom sitting on a silver surface. The attosecond tunneling current resolved that single atom while the electron wave packet remained laterally confined to roughly six angstroms, or six-tenths of a nanometer. They were looking at electronic behavior on the timescale where it actually happens without giving up the ability to distinguish an individual atom.
That gives researchers a way into processes that have always been difficult to catch from both directions at once. Electrons rearrange when charge moves through nanoscale devices, when quantum materials react to light, and during the electronic changes involved in chemical processes. Those changes don't wait around to be measured. They happen across distances of a few atoms and in slices of time so short that even light travels only a fraction of a micrometer.
The copper atom showed that those two scales can now be brought into the same measurement. Researchers can follow an electron through an interval measured in attoseconds and still keep an atomic-scale view of its wavefunction.
That's a very small place, for a very short time, and we can finally begin to watch what happens there.
These are interesting things, with JC.
Student Worksheet
Comprehension
What phenomenon allows an electron to cross an energy barrier in the STM junction?
How many attoseconds are contained in one femtosecond?
What role did the two delayed near-infrared laser pulses play in the experiment?
What did quantum simulations help the researchers determine?
What object did the researchers use to demonstrate atomic-scale spatial resolution?
Analysis
Why would improving temporal resolution be less useful if the electron wave packet became too spatially spread out?
Explain why the experiment's "space-time limit" should not be described simply as Heisenberg's uncertainty principle.
The experiment combined tunneling transients shorter than one femtosecond with angstrom-scale localization. Why is that combination scientifically important?
How does the copper atom experiment provide evidence that the technique retains useful spatial resolution?
Reflection
Humans cannot directly perceive either attoseconds or angstroms. How do instruments and mathematical models extend what scientists can investigate? Use at least two examples from the episode.
Difficulty Scaling
Level 1 — Foundational: Define the major vocabulary and identify what the microscope, laser pulses, and simulations contributed.
Level 2 — Applied: Explain relationships among tunneling, timing, field strength, and wave-packet localization using evidence from the transcript.
Level 3 — Advanced: Evaluate the experimental challenge of simultaneously preserving ultrafast temporal information and atomic-scale spatial information.
Student Output: Answer Questions 1–10 in complete sentences. Questions 6–10 should include specific evidence or concepts from the episode. Advanced responses should distinguish experimental evidence from interpretation.
Academic Integrity Guidance: Use the episode and assigned sources to develop your own explanation. Paraphrase rather than copying source language. Clearly identify any additional sources or AI assistance according to instructor requirements.
Teacher Guide
Quick Start: Introduce the scale vocabulary, play or read the episode once without interruption, conduct a second evidence-focused pass, then use Questions 6–9 for discussion before independent assessment.
Pacing Guide — Audio First
0–5 minutes: Bell ringer and scale prediction.
5–10 minutes: Preview femtosecond, attosecond, angstrom, wavefunction, and quantum tunneling.
10–16 minutes: First uninterrupted episode listening.
16–24 minutes: Second listening or transcript review; students record evidence about space and time.
24–36 minutes: Complete worksheet comprehension and analysis.
36–44 minutes: Discuss Questions 7–9.
44–50 minutes: Quiz or open-ended assessment and exit ticket.
Bell Ringer: If scientists can determine what happens to an electron extremely quickly but cannot determine where the behavior occurs, what information is missing? Reverse the situation and answer again.
Audio Guidance: On the first listen, ask students to identify the central scientific problem rather than record every number. On the second pass, have them note one time measurement, one distance measurement, and one experimental technique.
Audio Fallback: If audio is unavailable, read the transcript aloud or assign paired reading. Preserve the two-pass structure.
Time on Task: Approximately 45–50 minutes for a standard lesson; 70–90 minutes with extensions and assessment.
Materials
Episode audio or transcript
Student worksheet
Calculator or scientific notation reference
Paper or digital note-taking tool
Optional scale diagram from meters to angstroms and seconds to attoseconds
Vocabulary Prep
Reinforce 10−1510^{-15}, 10−1810^{-18}, and 10−1010^{-10} before discussing the experiment.
Contrast a classical trajectory with a quantum wavefunction without implying that the wavefunction is simply a physical cloud of ordinary matter.
Connect "tunneling" to crossing a classically forbidden energy barrier.
Misconceptions
"The electron drills a tunnel through matter." Quantum tunneling is not a physical hole being created in a barrier.
"Attosecond means the electron itself is extremely small." Attoseconds measure time, not size.
"The space-time limit is Heisenberg's uncertainty principle." The episode explicitly distinguishes the observed spatiotemporal coupling from the position-momentum uncertainty relation.
"Higher temporal resolution automatically produces better microscopy." The experiment demonstrates why temporal and spatial behavior must be considered together.
"The experiment photographed an electron like a conventional camera." The technique measures tunneling current and uses controlled fields and quantum modeling to investigate electron dynamics.
Discussion Prompts
What makes the phrase "watching an electron" potentially misleading if interpreted literally?
Why does the copper adatom provide an effective test of spatial resolution?
What does the experiment reveal that a static atomic-scale image cannot?
Where might simultaneous ultrafast and atomic-scale measurements become useful?
Formative Checkpoints
Students correctly convert 1 femtosecond to 1,000 attoseconds.
Students identify tunneling current as the measured electrical signal.
Students explain the function of the delayed light pulses.
Students distinguish temporal duration from spatial extent.
Students can state why the single copper atom matters to the demonstration.
Differentiation
Additional Support: Provide a scale ladder showing second → femtosecond → attosecond and meter → nanometer → angstrom.
Advanced Learners: Ask students to explain why photon-assisted and field-driven processes could produce different wave-packet behavior.
English Learners: Preteach barrier, tunneling, confined, pulse, current, and wave packet with diagrams and sentence frames.
Visual Learners: Have students sketch the STM tip, tunneling junction, sample, light pulses, and localized wave packet.
Assessment Differentiation: Permit foundational students to use a labeled diagram with explanatory sentences. Require advanced students to connect experimental design, observations, and scientific interpretation in a written response.
Time Flexibility: For a 30-minute lesson, use one listening, Questions 1–5 and 7–8, followed by the exit ticket. For a 90-minute block, add scientific-notation calculations and the extension activity.
Substitute Readiness: Provide the transcript, vocabulary list, Questions 1–10, and answer key. No laboratory equipment or specialized physics background is required.
Engagement Strategy: Ask students to draw a line representing how far they think light travels in one femtosecond, then calculate or discuss the actual scale after listening.
Extensions
Calculate approximately how far light travels in 1 femtosecond using d=ctd=ct.
Construct a scale comparison among 1 second, 1 femtosecond, and 1 attosecond.
Research one possible application of ultrafast microscopy in chemistry, materials science, or electronics.
Create a diagram explaining how an STM tip, sample, laser fields, and tunneling current interact in the experiment.
Cross-Curricular Connections
Mathematics: Scientific notation, powers of ten, unit conversion, scale.
Chemistry: Electron rearrangement, bonding, and charge transfer.
Engineering: Instrumentation, nanoscale electronics, and measurement design.
Computer Science: Computational simulations used to interpret experimental measurements.
SEL Connection: Emphasize productive uncertainty in scientific inquiry: researchers often improve knowledge by developing ways to measure phenomena that were previously inaccessible rather than expecting immediate certainty.
Skill Value Emphasis: Evidence interpretation, quantitative reasoning, model-based thinking, distinguishing related scientific concepts, and communicating across extreme scales.
Answer Key
Quantum tunneling.
1,000 attoseconds.
They created controlled, time-delayed electric fields that modified the tunneling barrier and allowed researchers to probe the electron response at ultrashort timescales.
They helped connect the measured signals with the underlying quantum dynamics and spatial behavior of the electron wave packet.
A single copper atom, or copper adatom, on a silver surface.
Excessive spatial spreading would reduce the ability to identify where atomic-scale electronic behavior occurred, undermining spatial resolution.
Heisenberg's familiar uncertainty relation concerns quantities such as position and momentum. The episode's space-time limit concerns how ultrafast driving and measurement relate to changes in the spatial distribution of an electron wavefunction.
It allows researchers to investigate electron dynamics on their intrinsic ultrafast timescale while retaining information at atomic dimensions.
The attosecond tunneling measurement could resolve the individual copper adatom while maintaining angstrom-scale localization.
Answers will vary but should explain that instruments convert otherwise inaccessible events into measurable signals and that quantum simulations help interpret those signals.
Quiz
Questions
What is the duration of one attosecond?
A. 10−610^{-6} second
B. 10−1010^{-10} second
C. 10−1510^{-15} second
D. 10−1810^{-18} second
What was modified by the controlled near-infrared fields in the experiment?
A. The atomic number of copper
B. The electron tunneling barrier
C. The speed of light
D. The chemical identity of silver
Why were quantum simulations important?
A. They replaced the physical experiment.
B. They converted copper into silver.
C. They helped connect measured signals to electron wavefunction dynamics.
D. They increased the size of the microscope.
What did the single copper atom experiment demonstrate?
A. Atomic-scale spatial information could be retained with attosecond-scale electron dynamics.
B. Electrons no longer exhibit quantum behavior at atomic scales.
C. Copper electrons move faster than light.
D. Scanning tunneling microscopy requires copper samples.
Which statement best describes the "space-time limit" discussed in the episode?
A. It is another name for the speed of light.
B. It proves that position and time form the standard Heisenberg uncertainty pair.
C. It concerns the relationship between ultrafast electron dynamics and the spatial structure of the wavefunction.
D. It establishes the smallest possible atom.
Assessment
Open-Ended Questions
Explain how the researchers combined scanning tunneling microscopy, controlled near-infrared pulses, tunneling-current measurements, and quantum simulations to investigate electron dynamics. Include both temporal and spatial resolution in your answer.
Why is resolving a single copper atom while measuring attosecond-scale tunneling significant? Construct a claim supported by at least two pieces of evidence from the episode.
3–2–1 Rubric
3 — Proficient: Scientifically accurate explanation; correctly connects experimental method, temporal resolution, spatial localization, and evidence; uses appropriate vocabulary.
2 — Developing: Demonstrates the central idea but contains an incomplete connection, limited evidence, or minor scientific imprecision.
1 — Beginning: Gives a partial description without clearly explaining the relationship between the experiment, spatial resolution, and temporal resolution.
Exit Ticket
In one sentence, explain why "faster measurement" alone does not describe the achievement.
Name one measurement scale from the episode and explain what it measures.
State one question that ultrafast atomic-scale microscopy might help scientists investigate.
Standards Alignment
NGSS — Science & Engineering Practices
HS-PS4-3 — Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model. Students distinguish quantum descriptions from classical particle trajectories and evaluate evidence involving light-driven electron behavior.
Developing and Using Models — Grades 9–12. Students use conceptual representations of the STM junction, tunneling barrier, electron wave packet, and laser fields to explain experimental observations.
Analyzing and Interpreting Data — Grades 9–12. Students interpret reported temporal and spatial measurements and use them as evidence for the capabilities of the microscopy method.
CCSS Reading
CCSS.ELA-LITERACY.RST.11-12.1 — Cite specific textual evidence to support analysis of science and technical texts. Students support worksheet and assessment explanations with evidence from the episode.
CCSS.ELA-LITERACY.RST.11-12.4 — Determine the meaning of symbols, key terms, and other domain-specific words and phrases. Students accurately use terminology including tunneling, wavefunction, attosecond, femtosecond, and angstrom.
CCSS.ELA-LITERACY.RST.11-12.7 — Integrate and evaluate multiple sources of information presented in diverse formats and media. Students connect audio narration, transcript evidence, quantitative scales, and conceptual models.
CCSS Writing
CCSS.ELA-LITERACY.WHST.11-12.2 — Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. Students explain the experimental method and significance using precise scientific language.
CCSS.ELA-LITERACY.WHST.11-12.9 — Draw evidence from informational texts to support analysis, reflection, and research. Students construct evidence-based responses from the episode and supporting scientific material.
C3 Framework — Inquiry
D2.His.10.9-12 — Detect possible limitations in various kinds of historical evidence and differing secondary interpretations. Applied as an evidence-literacy skill, students distinguish what was experimentally measured from interpretations based on quantum modeling.
D4.1.9-12 — Construct arguments using precise and knowledgeable claims, with evidence from multiple sources. Students formulate evidence-supported explanations of why combined spatial and temporal resolution matters.
ISTE / CTE — Applied Learning
ISTE 1.3 — Knowledge Constructor. Students evaluate scientific information and synthesize evidence into explanations of an emerging research technique.
CTE STEM Practice — Apply science and mathematics to engineering and technological problems. Students use scientific notation, scale analysis, instrumentation concepts, and model-based reasoning to interpret nanoscale measurement.
Career Readiness Competencies
Critical Thinking: Distinguish experimental observation from scientific interpretation.
Quantitative Literacy: Compare orders of magnitude across temporal and spatial scales.
Technical Communication: Explain a complex experimental method using accurate domain vocabulary.
Systems Thinking: Connect light fields, tunneling barriers, electron wave packets, measurement, and simulation as parts of one experimental system.
Homeschool / Lifelong Learning
Learners can independently explain the central experiment using evidence from the transcript.
Learners can use scientific notation to compare unfamiliar physical scales.
Learners can distinguish simplified analogies from more precise quantum-mechanical explanations.
Learners can connect fundamental physics research with applications in chemistry, materials, electronics, and quantum technology.
Show Notes
Researchers at the University of Regensburg and collaborating institutions have combined lightwave-driven scanning tunneling microscopy with attosecond-scale electron control to investigate electronic wavefunctions at extremely short times and atomic dimensions. Episode 1761 explores quantum tunneling, wave packets, near-infrared excitation, and the challenge of preserving spatial localization while examining faster electron dynamics. For classrooms, the story provides a concrete route into scientific notation, quantum mechanics, experimental design, evidence interpretation, and the relationship between fundamental physics and emerging technologies. It matters because many processes in materials, electronics, and chemistry begin with electron behavior occurring across only a few atoms and within fractions of a femtosecond.
References
Maier, S., Spachtholz, R., Glöckl, K., Bustamante, C. M., Lingl, S., Maczejka, M., Schön, J., Riedel, A., Richter, K., Giessibl, F. J., Bonafé, F. P., Huber, M. A., Rubio, A., Repp, J., & Huber, R. (2026). Tracking electrons at the space-time limit. Nature Photonics, 20, 961–967. https://www.nature.com/articles/s41566-026-01932-0
University of Regensburg. (2026, July 3). Microscopy at the space-time limit. https://www.uni-regensburg.de/en/research/home/news/latest-news/03-07-2026_microscopy-at-the-space-time-limit
University of Regensburg. (2026). Tracking electrons at the space-time limit [Institutional repository record and publication]. https://epub.uni-regensburg.de/79752/
Regensburg Center for Ultrafast Nanoscopy. (2026, July 3). Reaching the space-time limit. https://run-regensburg.de/2026/07/03/ultrafast-stm-at-the-run-reaches-the-quantum-mechanical-space-time-limit-for-the-first-time/
