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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 an 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 through 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 that 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 tunneling everywhere, in radioactive decay of course, but this 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 to the other 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 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 theory of special relativity explains that if you 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 its 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 you mean by “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 the new wavefunction as the cut-off front end
of the old 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 average
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.
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 the 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 this 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, naturally, 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 the 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.
Thank you to Brilliant for supporting PBS.
To understand astrophysics, Brilliant believes it helps to have a solid understanding of
relativity.
Brilliant has a lesson on special relativity that includes interactive challenges and problems
to solve.
A hands-on approach can guide you through thinking strategies for challenging subjects
like relativity.
It starts out explaining relativity in terms of boats passing by each other on a river,
then goes into some puzzles that require challenging perspective (like the ball stack bounce),
and then goes into the speed of light and even time travel!
To learn more about Brilliant, go to brilliant.org/Spacetime.
As always, if you've joined us on Patreon, I can't emphasize enough how helpful your
support is in keeping this show going.
But today I want to give a huge shoutout to our Big Bang supporter Henry Van Styn.
Henry, as a scientist I may not know everything about the depths of quantum tunneling, but
as a New Yorker I know that every tunnel needs a name so I’m proud to announce the Henry
Van Styn Quantum Tunnel.
It connects downtown Manhattan to … well, wherever you live right now so we can hang
out.
It goes through solid bedrock so there’s a low probability that your
quantum wavefunction will make it through - but if you do then the trip is instantaneous,
and so you get to avoid the downtown traffic.
Henry, you have our thanks and now you have our tunnel.
Please visit soon.
In the last episode we talked about why physicists believe magnetic monopoles.
You guys had your own strong opinions of questions and lots of questions.
MrRolnichek asks about the hedgehogs configurations - the radiating knots in the Higgs field that
might lead to magnetic monopoles.
They ask — if these can’t be removed by smooth variation in the vectors then how come
they're created in high energy events?
The answer is that at very high energies, the direction of the Higgs field becomes free
to vary wildly and adjacent points in the field are less coupled to each other.
Only when the field cools down to adjacent points become more tied to each other.
Any discontinuities that formed at high temperature can then be frozen into the field.
And Nate Underwood asks if the Higgs field can form so that there are no monopoles - no
discontinuities.
The answer is yes, but it’s extremely unlikely- - for the same reason that it’s increasingly
unlikely for a crystal to have no flaws the larger it is.
Try to make a flawless crystal the size of the universe.
Erik says that if magnetic monopoles are massive enough to collapse the early univeres, wouldn’t
we only find them inside black holes?
Well it depends on their density and whether inflation threw them apart faster than they
could find each other.
It’s certainly possible that magnetic monopoles to end up inside black holes, in fact some recent
work suggests that an individual magnetic monopole would manifest as a black hole - in
that it would have an event horizon.
However a monopole managed to get into a black hole, one thing is clear - it would still
behave like a monopole in that the black hole would radiate magnetic field lines.
Same as if the black hole held electric charge; it would produce an electric field.
And presumably if black holes had enormousmagnetic charges we’d see that in the way
they interact with matter.
As it is, the magnetic fields we observe around black holes seem more consistent with regular
dipole fields, with both north and south poles.
For example in the way they channel jets of material in opposite directions.
Wasko92 asks the real question.
Magnetic monopoles aside, why did Moody arrange for the whole Goblet of Fire thing when he could
have easily taken some of Harry’s blood on one of the numerous occasions that they met.
OK wasko92, I know this was supposed to be some hilarious non-sequitur with no relation
to the episode, but the jokes is on you my friend, because it's relevant to this episode
As everyone knows, Moody tricked Harry into touching the tri-wizard cup which was actually
enchanted into a port key that transported him and poor Cedric off Hogwart's campus.
It's hypothesized that portkeys are based on wormhole technology, but actually they may well use
quantum tunneling.
And that process actually evades Hogwart's security wards because the wizards are rubbish
at quantum mechanics.
I hope that clears things up for you.