# No, Quantum Tunneling Didn’t Break The Speed Of Light; Nothing Does

*The transition across a quantum barrier is known as quantum tunneling, and the amount of time it takes for such a transition to occur had never been measured before. For a single electron in a hydrogen atom, that timescale has now been measured to be no larger than 1.8 attoseconds, which is consistent with an interpretation of an instantaneous transition.*(AASF / GRIFFITH UNIVERSITY / CENTRE FOR QUANTUM DYNAMICS)

#### If you don’t look at the whole picture, it’s all too easy to fool yourself.

If you throw a tennis ball at a solid wall, it will strike the wall and ricochet back at you 100% of the time, just like you’d expect. In physics, a sufficiently strong barrier will prevent any incoming object from passing through it. But at the quantum level, this isn’t strictly true. If you replace a tennis ball with a quantum particle and a solid wall with any quantum mechanical barrier, there’s a finite probability that the particle will actually tunnel through the barrier, where it winds up being detected on the other side. It’s as though you threw the tennis ball at the wall and it went right through, unimpeded by the wall at all.

Scientists have, for the first time, successfully measured how long the tunneling process takes, and found that it was instantaneous. But this doesn’t mean it happened faster than the speed of light. Nothing breaks that speed, and here’s how you can see it for yourself.

*If you allow a classical particle, like a basketball or a tennis ball, to fall onto a hard surface like a table, you can be certain that it will bounce back. If you were to perform this same experiment with a quantum particle, you’d find, quite surprisingly, that there was a finite chance that it would tunnel through to the other side of the table, going through the barrier as if it were no obstacle at all.*(WIKIMEDIA COMMONS USERS MICHAELMAGGS AND (EDITED BY) RICHARD BARTZ)

When you think of the quantum Universe, chances are you think of tiny, individual particles all zipping around and colliding into one another. But one of the counterintuitive aspects of the quantum nature of reality is that this picture doesn’t quite explain what we observe. We know that there’s a fundamental uncertainty inherent to certain properties (like the positions) of quantum particles, and we can only describe them fully by using probability.

What this means is that if you take a single quantum particle, place it down at any one location, and ask “where is it now?” at some later time, you won’t find it simply by multiplying its speed by the amount of time that’s passed. The quantum nature of this particle means that its position is defined by a wavefunction, and that’s not well-determined. We can only give you the probabilities of where you might find it.

*As time goes on, even for a simple, single particle, its quantum wavefunction that describes its position will spread out, spontaneously, over time. This happens for all quantum particles.*(HANS DE VRIES / PHYSICS QUEST)

This bizarre, counterintuitive property of quantum physics isn’t a limitation of our measurement equipment, but rather is a fundamental property of our reality and the rules that govern it. Whether you’re talking about:

- a particle at rest,
- a free particle traveling through space,
- a bound particle (like an electron in an atom) that’s restricted as far as where it’s allowed to be,
- or a particle that encounters an obstacle that restricts what quantum states it’s allowed to occupy,

there are no certainties until you make a measurement, only probabilities.

*Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wavefunction solutions to the Time-Dependent Schrodinger Equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (B,C,D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E,F) are non-stationary states, solutions to the Time-Dependent Schrodinger equation.*(STEVE BYRNES / SBYRNES321 OF WIKIMEDIA COMMONS)

So you might think, if you have a system that has a probability of tunneling from one side of a quantum barrier (like bound in an atom, or in a false minimum) to the other, there would be a restriction on how quickly that transition could occur. Maybe it would depend on the size of the barrier, the thickness of the barrier, or some other factor that was related to its physical properties. After all, in this Universe, everything should be limited by the speed of light.

The simplest setup of all is to take one single particle, like an electron, bound in a restricted system, like a hydrogen atom. There’s a finite, non-zero probability that it will tunnel to an unbound state. By imaging it with the proper equipment — ultra-fast photons, for instance — you can accurately measure the time interval it takes to tunnel from a bound to an unbound state.

*A scalar field φ in a false vacuum. Note that the energy E is higher than that in the true vacuum or ground state, but there is a barrier preventing the field from classically rolling down to the true vacuum. It is possible to arrive in the true vacuum state, however, via the process of quantum tunneling.*(WIKIMEDIA COMMONS USER STANNERED)

Researchers at the Australian Attosecond Science Facility have done exactly that, finding that this simplest of transitions takes at most 1.8 attoseconds (1.8 × 10^-18 s). That means, at the speed of light, we’re talking about traveling a distance of just 5.4 ångströms. According to Robert Sang, one of the lead researchers:

There’s a well-defined point where we can start that interaction, and there’s a point where we know where that electron should come out [the interaction itself is] instantaneous. So anything that varies from that time we know that it’s taken that long to go through the barrier… It came out to agree with the theory within experimental uncertainty being consistent with instantaneous tunneling.

While this has fascinating implications for the practical applications of, say, the construction of a quantum-limited transistor, “instantaneous” in this context doesn’t mean that it violates Einstein’s relativity.

*When a quantum particle approaches a barrier, it will most frequently interact with it. But there is a finite probability of not only reflecting off of the barrier, but tunneling through it. Although this new research implies that the step of tunneling itself is instantaneous, that doesn’t mean you can cross from one side of the barrier to the other in a time that’s less than the light-travel time.*(YUVALR / WIKIMEDIA COMMONS)

It isn’t as though at one instant you can say “this particle is over there” and then, some tiny amount of time later, you can say “this particle is now located here instead” with that change-in-distance divided by the change-in-time exceeding the speed of light. The experiment, which is remarkable for how precise and clean it was in only involving a single particle in a single, bound system, simply shows that there’s no fundamental quantum delay in this tunneling transition.

But it also helps expose how physicists have managed to exploit a many-particle system in order to create the illusion of something traveling faster than light: a result which gets misreported every few years in the popular media. Imagine you’ve got a set of quantum particles, bunched together into a tight pulse, tunneling or otherwise traveling through a barrier of some sort.

*By firing a pulse of light at a semi-transparent/semi-reflective thin medium, researchers can measure the time it must take for these photons to tunnel through the barrier to the other side. Although the step of tunneling itself may be instantaneous, the traveling particles are still limited by the speed of light.*(J. LIANG, L. ZHU & L. V. WANG, LIGHT: SCIENCE & APPLICATIONSVOLUME 7, 42 (2018))

It’s truly remarkable at how successful we’ve become at imaging pulses that move at speeds that approach or even equal the speed of light, thanks to novel techniques and technologies. What you can do is measure:

- where this pulse is located in space at a certain instant in time, before it encounters a barrier,

*When you create a pulse of particles, whether those particles are massive or massless (like light itself), there is always a distribution in space and time inherent to those particles.*(E. SIEGEL)

- where and when you expect that pulse to arrive if it were to move at the speed of light and successfully tunnel through the barrier,

*Naively, if you sent particles from one location to another without a barrier or something to filter them out in between, you’d expect they would arrive at your destination in a predictable amount of time that was set (or at least limited) by the speed of light.*(E. SIEGEL)

- and then comparing your measurement for where the pulse is located in space at a later instant in time, after successfully tunneling through the barrier.

It might surprise you to learn that the pulse that you detect on the other side of the barrier can easily be found appearing to move faster than the speed of light would seem to permit!

*If all you did was measure the start position and time and end position and time of a set of particles that were sent towards and wound up passing through a quantum barrier, you might (falsely) conclude that these arriving particles had traveled faster than the speed of light. Don’t worry; they didn’t.*(E. SIEGEL)

You might think, based on what you just read about the speed of quantum tunneling being instantaneous, that this means that particles can travel infinitely fast, breaking the speed of light, through a quantum mechanical barrier of finite, non-zero thickness. That’s the misinterpretation that always crops up, and how people fool themselves (and unscrupulous news organizations try to fool you) into thinking they’re breaking the speed of light.

But all that’s happening here is a portion of the quantum particles found in the pulse tunnels through the barrier, while the majority of the particles does what tennis balls do: they bounce back, failing to arrive at the destination. If you can front-load which particles make it through the barrier, preferentially cutting off the particles in the back of the pulse, you’ll falsely measure a faster-than-light speed, even though no individual particle actually breaks the speed of light.

*If you were to somehow track the individual motion of each and every particle that you launched towards your destination, you’d find that the ones that made it were simply part of the front-end of the initial pulse, and that no actual particles were traveling faster than light itself.*(E. SIEGEL)

So what does this new result actually mean, then?

Simply that the actual process of tunneling itself, where the transition occurs from being in a bound state on one side of a quantum barrier to an unbound sate on the other side, doesn’t take any extra, additional time on top of all the other physical effects. Moving a certain distance in a given time is still limited by Einstein’s relativity, though, with this restriction applying to each and every particle under all circumstances. It’s an incredible feat that scientists have made this measurement directly, for a single particle, and demonstrated that there is no delay inherent to the tunneling process itself.

But going faster than light? That’s still restricted to the realm of science fiction alone.

*Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.*