Aephraim Steinberg (University of Toronto) leads experiments on how long particles spend inside barriers and media, and his group has measured quantities with the dimensions of time that turn out to be negative — not as a mathematical curiosity, but as a value that appears in multiple, seemingly unrelated physical contexts, suggesting it may reflect something real about quantum processes.
Negative time: what it is and isn’t
The basic setup: send a photon (or other particle) toward a medium or barrier, detect it on the far side, and ask when it is most likely to arrive and how long it spent inside.
Classical expectation: if the peak of a pulse exits earlier than it “should,” that can be explained away as selection bias — for example, only the front part of a wave packet gets through an absorbing medium, so the average arrival time of the survivors is earlier, even though nothing traveled faster than light.
Historical background: Sommerfeld and Brillouin showed in the early 20th century that, despite such negative-time formulas, no information or energy travels faster than light, so causality is safe.
The new surprise: Steinberg’s group looked not at when the photon arrives, but at how long the atoms in the medium spend in an excited state — an indirect probe of what happened inside the barrier, analogous to measuring carbon monoxide left behind by cars in a tunnel.
For transmitted photons, the atoms behaved as if they had spent less time excited than if no photon had been there at all — a negative “dwell time.”
This cannot be explained by the classical selection-bias story; it suggests the negative time is not just an artifact of reshaping a wave packet, but is connected to a real physical quantity.
Why a resonant atomic medium matters
The experiment uses a cloud of rubidium atoms and laser light tuned on resonance, so that each photon has a significant chance of being absorbed and re-emitted.
On resonance, the usual “slow light” picture (photon absorbed, atom sits excited for a while, photon re-emitted) breaks down, and the traversal time can become negative.
By using a second probe beam, the experiment measures the state of the atoms (how much time they spend excited) conditional on whether a given photon was transmitted or reflected.
The key result: the negative traversal time of the photon equals the negative excitation time of the atoms, even though these are defined and measured in completely different ways.
Multiple velocities of light
The episode distinguishes several notions of “speed” for light in a medium:
phase velocity — speed of wave crests
group velocity — speed of the pulse envelope, often associated with energy transport
signal / information velocity — how fast a message can be sent
front velocity — the earliest moment any disturbance can arrive; this never exceeds c
In absorbing or tunneling media, group velocity can exceed c or become negative, but information and front velocity do not.
There is no single, universally agreed-upon definition of energy velocity in these situations; different definitions can disagree, and some textbook formulas even give superluminal energy speeds in certain transparent, amplifying media.
Time in quantum mechanics: parameter, not observable
In both classical and quantum physics, time is a parameter, not an observable: we ask “what is the position at time t?” but not “what is the time at position x?”
Measuring a time interval always reduces to correlating one observable (e.g., the position of a clock hand) with another event.
Because of this, there are multiple, inequivalent ways to define “how long” a particle spends in a region, which coincide classically but diverge quantum mechanically.
Weak measurements and conditional averages
Weak measurement (Aharonov, Albert, Vaidman, 1988) is a technique for extracting average properties of a system without strongly disturbing it, by coupling the system weakly to a meter and averaging over many trials.
What makes it powerful is post-selection: one can ask, “for those particles that were later found at this detector, what was the average value of some quantity earlier?”
This allows quantum-mechanically meaningful statements about what the system was doing between preparation and final measurement, something standard textbook quantum mechanics discourages.
Bohmian trajectories observed
In a double-slit experiment, Steinberg’s group used weak measurements of position, post-selected on where particles landed, to reconstruct average trajectories through the slits.
These trajectories match those predicted by Bohmian mechanics, a hidden-variable theory in which particles have definite positions guided by a wave.
This does not prove Bohmian mechanics correct — it is constructed to agree with standard quantum mechanics — but it shows that the “hidden” trajectories correspond to a measurable flux operator, making them experimentally accessible rather than purely metaphysical.
Heisenberg’s disturbance argument is misleading
The usual story — that the uncertainty principle arises because measuring position necessarily disturbs momentum — is a useful picture but not the full truth.
The rigorous uncertainty relations (Robertson, Schrödinger) are properties of quantum states, not of measurement disturbance.
Ozawa showed, and Steinberg’s group confirmed experimentally, that the disturbance due to a specific measurement can be smaller than Heisenberg’s original bound, once disturbance and error are properly defined.
Bell’s inequalities and locality
Bell’s theorem shows that no local hidden-variable theory can reproduce all quantum predictions.
Steinberg notes that there is still debate about exactly what is ruled out: some researchers (e.g., Brassard, Deutsch–Hayden) argue that a weaker notion of locality can be preserved if one is careful about how information is defined.
The mainstream view is that Bell violations imply nonlocality, but the episode emphasizes that the interpretation is still contested among experts.
Quantum information and the future of quantum mechanics
The biggest open practical problems in quantum information are:
building a large-scale, fault-tolerant quantum computer
identifying which problems such a computer would actually solve better than classical machines
On the foundational side, a key frontier is complexity: can quantum mechanics really describe systems of arbitrary size and complexity, or does it break down for macroscopic or gravitating systems?
Some researchers (e.g., Penrose) expect gravity to cause breakdown; others (e.g., Deutsch, Vaidman) favor a many-worlds view in which the Schrödinger equation never breaks down and classicality emerges from decoherence and complexity.
Steinberg’s current focus
He is working on tunneling-time experiments with Bose–Einstein–condensate atoms fired at a light-sheet barrier, using weak measurements (a Larmor clock) to ask how long transmitted atoms spend inside the barrier.
A new theoretical result suggests that strongly measuring whether a particle is inside the barrier can, under certain conditions, collapse the state and enhance transmission, and that the required measurement speed defines a new timescale for tunneling.
This connects to a broader theme: how much can be said about the history of a quantum system, and how measurement itself shapes that history.
