Paradoxically, the most promising prospects  for moving matter around faster than light   may be to put a metaphorical brick wall in its  way.

New efforts in quantum tunneling - both   theory and experiment - show that  superluminal motion may be possible,   while still managing to avoid the  paradox of superluminal signaling.

Quantum tunneling is one of the weirder  phenomena in the generally very weird   world of quantum mechanics.

It describes how  quantum particles are able to move across   seemingly impenetrable barriers - for example,  when atomic nuclei decay.

But it’s not just the   Houdini-like power that makes the quantum world  weird - it’s also that the tunneling motion   may move particles faster than  they could travel if the barrier   wasn’t there - and even faster than  light could traverse the same distance.

Now we covered quantum tunneling a long LONG  time ago - in fact it was the first video   we did on quantum mechanics.

But things have  actually evolved in the 5 years since.

I mean,   we’ve learned a lot on this show and so we can dig  deeper into the FTL aspect of quantum tunneling.

But there’s also new science, and so today  we’re going to look at a new theoretical   result and a new experiment that are  bringing us closer to understanding   the superluminal prospects of quantum tunneling.

But first, a quick recap of quantum tunneling.

Imagine  you’re driving a car towards a steep hill when the   engine cuts out.

You can still make it over the hill if you have enough speed - enough kinetic   energy to see you to the top.

But if the car isn’t moving fast enough then it’ll inevitably   slow down and roll back.

There’s nothing in the  laws of physics that could allow you to reach   the other side of the hill.

Well, nothing  in the laws of classical physics anyway.

A similar thing happens in the  world of quantum mechanics,   where particles are pushed and  pulled by the fundamental forces,   forming energetic hills and valleys - a landscape  of so-called potential barriers.

For example, the   protons and neutrons in the atomic nucleus are held  in the potential barrier of the strong nuclear   force.

If one of these particles had enough energy  it could punch through that barrier.

Fortunately   for the stability of atoms, nucleons mostly  remain trapped.

Mostly.

In radioactive decay,   particles that should never have enough energy  to escape the nucleus are found to leak out.

This is quantum tunneling.

The key  to the escape is quantum uncertainty.

Between observations, quantum particles don’t  have well defined properties - and that includes   their positions.

We represent the location of,  say, a proton in a nucleus as a wavefunction.

It’s an abstract wave that encodes the  information of where the proton might be.

Upon measurement, or upon interaction with  another particle, the proton can end up   anywhere within that wavefunction, with  some locations more likely than others.

To understand what happens when a proton bounces  around inside a nucleus, we need to see how its   wavefunction evolves according the the Schrodinger  equation - which is just the equation of motion   of wavefunctions.

This equation tells us that the  wavefunction is mostly reflected or scattered back   by the wall of the nucleus.

But the Schrodinger  equation is very clear that this isn’t the only   thing that can happen.

Due to the blurred-out  nature of the wavefunction, a small part of it   leaks out to the other side.

The proton  ends up being simultaneously reflected back   and transmitted through the barrier.

Now the  latter is very improbable - only as likely as   the tiny fraction of the wavefunction  that peaks through the barrier.

But improbable isn’t impossible, and so if  you then observe the nucleus, it’ll “collapse”   into one of those two states - either  business as usual, or a nuclear decay.

We see quantum tunneling everywhere, Radioactive decay of course, but tunneling also drives   many other important processes.

It’s necessary for  the nuclear fusion reactions that power the sun,   in some biological processes, and it’s  even a critical part of the working of   transistors and other electronic components.

But even with the ubiquity of this phenomenon,   we know very little about what happens during  the tunneling event itself.

For example, is the   transition of the particle from one side of the  barrier instantaneous, or does it take some time?

It turns out it’s very hard to determine  the so-called tunneling time because,   in the fuzzy world of quantum mechanics,   it’s hard to even define what we mean by  tunnelling time or time for that matter.

One thing however is clear at least - for a number of  definitions of tunneling time, faster-than-light   movement, really does seem to be a thing.

This  was first shown by the physicist Thomas Hartman   in 1962, who found that for one definition,  the time taken to tunnel can become independent   of the thickness of the barrier.

In other words,  you can double the length of your barrier, and   your particle will take the same amount of time  to travel all the way through.

For a thick enough   barrier, this ‘Hartman effect’ can effectively  teleport real, physical matter between locations   faster than it would take to travel that distance  sans barrier - even at the speed of light.

Now, our old pal Professor Einstein is not a fan  of faster-than-light motion.

As we’ve said before,   his special theory of relativity explains  that if you can move faster than light,   you can send signals into the past, and create  a whole bunch of paradoxes.

So in our previous   tunneling episode, we offered an explanation  for why this effect doesn’t break relativity.

It came down to the definition of tunneling time.

If the position of the tunneling particle isn’t   perfectly known, how do we know when to start and  stop our tunneling stopwatch?

It seems natural to   define those times as whenever the center of the  wavefunction passes the start and end points.

But what if the wavefunction  changes during the tunneling.

In a sense, the leading edge of the old  wavefunction becomes the center of the new wavefunction.

It’s like if you measured a train’s travel  time through a tunnel by clicking a stopwatch   as the center of the train passed  the entrance to the tunnel,   and then again when the front  of the train reaches the exit.

You’ll get a shorter time than if you clicked  for the same point at both tunnel ends.

Now if this was a quantum-tunneling train, then  only the front carriage would make it through the   tunnel, while the rest of the train would be  reversed and travel back the way it came.

And   then when you observe the train, all  but one of the carriages would vanish!

It’s hard to measure the travel time of a quantum  train OR a quantum wavefunction because it’s hard   to define the start and end points.

Certain  definitions seem to imply faster than light   motion.

But that’s also true of motion without  a barrier.

Launch a particle through empty space   with a well defined starting position, and it’s  position wavefunction will spread out before the   finish line.

The center of that wavefunction  can’t travel faster than the speed of light,   but upon measurement, the particle may appear to   be at the leading edge of the wavefunction  - potentially nudging it above light speed.

So you can see how the question of tunneling  time is a bit messy.

If we want to answer this,   we need to define a better question.

Let’s instead ask the following:   is it possible to send a message between  two points that are separated by a barrier   faster than you can transmit the same message  through empty space?

Fortunately a recent paper   helps us answer exactly that from a theoretical  standpoint.

Most previous work on tunneling time   relied on the Schrodinger equation, which  doesn’t incorporate Einsteins’s special theory   of relativity and so has no speed limit baked into it.

These new guys use the Dirac equation, which properly   incorporates special relativity and so we can  take any emerging FTL motion more seriously.

The explanation boils down to a thought  experiment.

Imagine you try to send a message   encoded in a collection of particles to a friend,  and you want it to arrive as soon as possible.

Should you send the message through  empty space, or through a barrier?

Can quantum tunneling really speed up the  transmission of the information contained   in that message?

Well it turns out that the answer  depends on what it means to “receive the message”.

If you can count the message received at  the instant the first particle arrives,   then the new study finds that the  tunneling message really does arrive first.

And the thicker the barrier, the  bigger the difference in arrival time.

That’s just what Hartman calculated using  arguably the wrong equation back in 1962.

The study also finds that the tunneling wave  packet isn’t necessarily “reshaped” all that   much - it’s not clear that we can really think of  it as the cut-off front end of the wavefunction,   or the first carriage of the quantum train.

So FTL verified, right?

Not quite.

The  study finds that the average travel time   for tunneling particles is shorter than the time  the free-flying particles.

But that’s only for the   tunneling particles that make it through.

Most get  reflected by the barrier, and as the barrier gets   thicker, exponentially more get reflected  until only a miniscule number pass through.

If you try to send your message over and  over, your friend will most likely receive   a free-flying particle long before they receive  a tunneling particle - staggeringly more likely   for any meaningful distance, and that’s just  because the former is much more likely to make it.

So does this really save causality?

In  order to violate causality, your friend   would need to send a return message that  was influenced by your message to them,   which could then cause a paradox loop.

The  authors say that more work is needed to verify   that this is ruled out, but in general  it looks like a lifeline for causality.

All this theoretical stuff is good and  fun, but what does experiment have to say?

Efforts from the early 80s and on seemed  to agree that the Hartman effect is real,   but interpretation of the results suffer from  some of the same problems as the theoretical   calculations - how do we define the  tunneling time?

And even trickier,   how do we define a tunneling time  that we can actually measure?

For a real, physical experiment, we need a  clock that’s physically measurable.

In 2020,   a paper was published in the journal  Nature that used the swiveling axis of   a particle’s quantum spin as a clock hand.

The phenomenon is called Larmor precession,   in which a particle’s dipole magnetic field, which  is defined by its spin axis, precesses like a top   in an external magnetic field.

The rate of  rotation can be used as an internal clock.

In their experiment, they fired  ultracold rubidium atoms at a laser field   that was spread out over a small area.

That field  was strong enough to deflect the atoms completely,   and so provided an insurmountable barrier.

Some particles did manage to   tunnel through anyway.

For those ones, their spins  were altered by the magnetic field of the laser,   and the longer they spent inside the  barrier, the more their spins changed.

So, ok, what did they find?

Did their  particles travel faster than light?

Well… no,   but they weren’t trying to make them do  that.

They were just trying to verify whether   using spins as an internal clock would  work at all, and they were successful.

The spins were altered by pretty much the same  amount that theory predicted they would be.

But the results are still relevant  for the faster-than-light Hartman effect,   because the spin-based clocks that they were  working with should still show the effect under   FTL circumstances, with faster particles and a  thicker barrier.

The point is that the theory   and the experimental tools are now converging on  a way to answer our questions once and for all.

Is faster-than-light motion or influence possible?

Perhaps yes, but it seems only in cases where   faster-than-light signaling is impossible.

Because as we’ve discussed many times before,   when it comes to the speed of light, the house  always wins.

All signals in our universe,   whether via quantum tunneling or quantum  entanglement, seem to be bound by the same   limits imposed by relativity.

The universe  insists that we take the long way around,   and as fast as we can find them it seals  up any new shortcuts through spacetime.