The Hartman effect
In quantum mechanics, particles can pass through a barrier even if they do not have enough energy to go over it. This process, called quantum tunneling, is essential for phenomena like nuclear fusion in the sun and the operation of flash memory. A persistent question since the 1930s has been: how long does this tunneling take? The answer has strange results that appear to challenge one of physics' most fundamental limits.
In 1962, physicist Thomas E. Hartman made a startling theoretical prediction. He calculated that as a barrier gets thicker, the time it takes for a particle to tunnel through it does not increase. Instead, it levels off to a constant value. This phenomenon is now known as the Hartman effect. The implication is that for a sufficiently thick barrier, a particle could effectively travel from one side to the other faster than light could travel the same distance in a vacuum. This calculated speed-up doesn't just suggest faster-than-light travel; it makes it unavoidable under certain conditions.
Decades of experiments have confirmed that the Hartman effect is real. In one famous experiment, Günter Nimtz and his colleagues at the University of Cologne transmitted microwaves carrying Mozart's 40th Symphony through a barrier. They reported the signal traveled at 4.7 times the speed of light over a distance of 11.4 centimeters. More recent, precise measurements continue to verify superluminal, or faster-than-light, tunneling speeds. In 2020, a team led by Aephraim Steinberg at the University of Toronto measured how long rubidium atoms spent inside a 1-micron-thick laser barrier. The average time was just 0.61 milliseconds, a duration shorter than it would have taken the atoms to cross the same distance in empty space.
Causality and communication
The prospect of faster-than-light travel raises immediate concerns about causality—the principle that a cause must precede its effect. If information could be sent faster than light, it would be possible in some reference frames to receive a reply before the original message was even sent. However, physicists generally agree that quantum tunneling does not allow for such a violation.
The consensus is that while the peak of a particle's wave packet can indeed appear on the other side of a barrier superluminally, this cannot be used to transmit controllable information faster than light. The front of the wave, which would carry the actual new information, never exceeds the speed of light. The barrier acts like a filter, reshaping the wave packet by amplifying its leading edge. This gives the illusion of the peak arriving "early," but no part of the signal that could carry a message breaks the light-speed limit.
The debate is far from settled, with physicists proposing at least 10 different mathematical definitions for what "tunneling time" even means. Some recent experiments have measured results that appear to be negative time. A University of Toronto team measured the time atoms spent in an excited state as a photon passed through, and the result was a negative number. This does not mean time travel is possible, but rather that our classical intuitions about time and duration do not apply cleanly at the quantum level. The mystery of tunneling time continues to be an active area of research.