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They say that a watched pot never boils.
This has now been proven true by quantum mechanics.
“A moving arrow is at rest.”
This is obviously a nonsensical contradiction.
But Zeno, Greek philosopher famous for his metaphysical trolling, devised a paradox whose
conclusion is just this.
Here’s how it goes: if you look at an arrow flying through the air at any instantaneous
snapshot in time, the arrow doesn’t travel any distance.
If time is composed of an infinite number of these snapshots, and the arrow doesn’t
move in any of them, then the arrow is at rest during the entirety of its flight.
The moving arrow is at rest.
Nowadays, most physicists and mathematicians don’t really see Zeno’s arrow as paradoxical.
We think of an instant as a vanishingly small interval of time, then during that time
the moving arrow travels a vanishingly small distance - but the “vanishingly small”
part cancels out and the arrow’s instantaneous velocity is very real.
That’s what a mathematician might tell you - but quantum mechanics also has a thing or
two to say about extremely tiny distances and time intervals.
In fact, if we’re talking about a quantum arrow, there may be a way to freeze its motion
simply by looking at it, through the aptly named quantum Zeno effect.
The quantum Zeno effect predicts that certain quantum events - like the electrons moving
between atomic energy levels, or the decay of atomic nuclei, can be frozen through the
simple act of observation.
I’m going to tell you about some very real experiments that claim to have demonstrated
this phenomenon.
But first, let’s see if the Quantum Zeno Effect can save us from being shot by a quantum
arrow.
First we’ll give our arrow a few weird behaviours befitting a good quantum object: we have quantization
- certain properties of our arrow can only take on specific, discrete values - like how
an electron can only occupy certain energy states in an atom.
In this case let’s say our quantum arrow’s position is quantized - it can exist only
at the start and end of its path, but not in between.
In order to travel from start to end, it has to flick between these states without occupying
intervening space.
One way to do that is by executing a quantum jump, which we discussed in our recent episode.
OK, the next quantum property we need is superposition.
Just like Schrodinger’s cat,
our quantum arrow can exist in multiple states at once.
That means it can be at the start and end of its path simultaneously.
It could be 50-50 split between the two, or 25% in one, 75% in the other, etc.
Now, you never actually see it in both states at once.
Rather, each state has an amplitude that determines the probability of finding the arrow in that
state were you to try to observe it.
In the language of the Copenhagen interpretation of quantum mechanics, we say that the “wavefunction
collapses” on observation.
Prior to that observation, the arrow exists as just the distribution of probability amplitudes
of its position; its wavefunction is spread between the start and end of the trajectory.
But after observation it collapses to definitely one or the other - at least, according to
Copenhagen - and we’ll be coming back to this craziness later.
This superposition thing actually gives our quantum arrow a way to travel its path smoothly
and gradually, but still without occupying the space in between.
And maybe for us to save ourselves in the end.
Here’s the scenario: someone shoots a quantum arrow at you.
It begins in the pure state of being entirely at the start of its journey, but then it enters
a superposition of states - mostly at the start, but also a little bit at the end.
If you observe the arrow now, most likely it’ll “collapse” to the starting position,
but there’s a small chance it would suddenly appear at the final state - having reached
you.
But if there’s no observation the wavefunction evolves - less and less amplitude at the starting
state and more and more at the end state - until it finally enters the pure state of definitely
hitting you.
Two ways this can play out: the arrow leaves the quantum bow with a quantum twang.
In shock you close your eyes for a second, which is your mistake - it allows the arrow’s
wavefunction to evolve smoothly into the state of quantum ouch.
But what if you keep your eyes open?
Every observation you make of the arrow collapses its wavefunction into one of its possible
positions - start or end.
But because you start watching it close to the beginning of its journey, there’s very
little probability of it collapsing to the end.
Your observation resets the trajectory to the start, at which point the wavefunction
has to start evolving from scratch - but you keep observing it and keep resetting it back
again through the magic of the Quantum Zeno Effect.
So the message is clear - if anyone ever tries to shoot you with a quantum arrow, don’t
blink.
Of course arrows don’t really behave this way, but it seems that this is exactly what
real quantum systems should do.
If a system can occupy two discrete states and transition between those states, that
transition can be halted if you continuously measure the state - again, in theory.
This has actually been tested for electron transitions in atoms - and I’ll tell you
about the experiments in a minute.
But in principle this would also work for radioactive decay, even chemical reactions
The basic idea of the quantum Zeno effect was first proposed by Alan Turing, but it
got a full theoretical description in the 1970s.
And then in 1990, a group of scientists headed up by David Wineland and Wayne Itano claimed
to have demonstrated it in an experiment by halting electron energy transitions.
These were some of the same people who first demonstrated quantum jumps, and using a similar
scheme that we described in that episode.
To recap - we have a collection of laser-cooled atoms in an electromagnetic trap.
A constant radio-frequency field is tuned to cause electrons to oscillate smoothly between
two energy levels - call them 1 and 2.
Just like our quantum arrow, sometimes an electron is in state 1, sometimes state 2,
but in between it’s a smoothly-varying superposition of both.
Next they flash the atoms with a laser whose frequency matches the energy difference between
state 1 and a new state, state 3.
If the electron is in state 1 when the laser pulse hits, it absorbs a laser photon and
jumps to 3, and then immediately drop back down to 1, releasing the energy as a new photon
that the researchers can detect - so the atoms glow during these laser pulses.
On the other hand, if the atom is in state 2 during the pulse, it would not absorb a
photon and the atom would stay dark.
But what if the laser hits while the electron is in the middle of a transition - in a superposition
of states 1 and 2?
According to the wavefunction collapse picture, it has to make a choice - the superposition
must vanish and the electron will be seen in either state 1 or state 2.
According to the researchers, the laser acts like a measurement - and remember, measurement
should be able to freeze quantum arrows and presumably also electron transitions via the
Quantum Zeno Effect.
To test this, the researchers start the atoms all in state one, and then hit them with a
series of very rapid laser pulses.
In theory, if these “measurements” are fast enough they should stop the wavefunction
from evolving.
And they report that it did exactly this.
The faster the chain of pulses, the more likely that atoms remained in state 1 - which they
could check with one final pulse to see if the atoms still glowed.
Long story short: it appears you can freeze a quantum state by measuring it continuously.
Further studies have claimed successful observation of the quantum Zeno effect, including various
studies of atomic energy levels, as well as the freezing of quantum tunneling - the same
phenomenon that allows particles to “teleport” out of nuclei during nuclear decay.
It’s even been proposed that the quantum Zeno effect plays a role in the photochemical
reactions that give birds their ability to see magnetic fields - something we’ve talked
about before.
So there we have it.
Quantum Zeno effect verified?
Well, not quite.
A flurry of papers came out after the 1990 result disputing the claim on various grounds,
and the arguments have continued.
But I want to highlight one particular point.
The physicist Leslie Ballentine argued that it’s not the abstract act of measurement
that causes the quantum Zeno effect, but rather it’s a physical consequence of interacting
with the system.
In this case, hitting the atoms with a laser pulse.
Ballentine’s objection gets to the very foundations of quantum mechanics: what exactly
do we mean by a “measurement” and what do we mean by wavefunction collapse?
Let’s start with measurement.
It’s never possible to perform a measurement without interacting with a system, and that
interaction has consequences beyond just increasing our knowledge.
If the measurement interaction is subtle enough then you might hope to gain that info without
perturbing the system too much.
Ballentine showed that each laser photon perturbed the system in such a way that the electron
had an increased chance to jiggle back to its starting location.
And to achieve a true quantum Zeno-like freezing you’d need to hit the atom with many, many
photons - and that was certainly not a “subtle” measurement.
Recently, a group of researchers from Washington University claim to have proved that it’s
perturbation, not measurement, that causes the quantum Zeno effect by demonstrating that
with the right type of “jiggling” a quantum transition could be forced to speed up rather
than to freeze - in what’s called the anti-Zeno effect.
Another way to think about measurement is in terms of how much information it extracts
from the system.
The idea is that measurement causes wavefunction collapse because it scrambles the delicate
information connecting different parts of the superposition.
Superposition only exists if the different parts of the wavefunction are connected or
correlated with each other.
We would say that the wavefunction for different electron states or quantum arrow positions
are in phase with each other, or “coherent”.
But that coherence is easy to mess up.
Any interaction causes information to quickly spread into the environment.
Decoherence occurs, and the different parts of the wavefunction, representing possible
realities, can no longer interact.
In fact, as argued by Ballentine, you can force a quantum system back to its starting
state without true decoherence.
But to get a full quantum Zeno effect - a perfect freezing of your electron or quantum
arrow - you need to perfectly measure it, and that means decoherence - or the illusion
of wavefunction collapse.
So on to wavefunction collapse.
In the Copenhagen interpretation, only the part of the wavefunction corresponding to
the measurement outcome survives.
But in the Many Worlds interpretation, the entire wavefunction survives and splits and
you split with it.
Obviously we’ve talked about decoherence and many worlds before, but let’s talk about
what the quantum Zeno effect looks like in this picture.
The effect should still exist, because Many Worlds gives the same predictions as Copenhagen.
But in this case, you’re not forcing the wavefunction to collapse back to its starting
position through the power of observation.
Your interaction with the wavefunction causes it to decohere - which means two things - you
perturb the system in a non-subtle way.
For example, by forcing the electron or quantum arrow out of its superposition.
In Many Worlds, that means generating separate realities corresponding to the possible outcomes.
If you do it right you’ll produce more “worlds” in which the system goes back to its starting
state.
And then you enter the world of of the possible outcome states - again, most likely the starting
position.
But if your observation wasn’t perfect, there’ll be some worlds in which the final
state is chosen rather than the starting state.
Like I said, if someone shoots you with a quantum arrow, don’t blink.
The quantum Zeno effect appears to be very real - but its interpretation is still hotly debated.
And perhaps some of this is just semantic - for example, how do we really define measurement
and interaction?
And what is wavefunction collapse?
But quantum zeno experiments are difficult, and perhaps future brilliant tests will give
us clues to unravel the deepest mysteries at the heart of quantum mechanics.
So there you have why a watched quantum pot never boils.
And it's because you did watch space time.
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Last time we gave you an update on the crisis in cosmology - the tension between the expansion
rate of the universe measured at the beginning of the universe with the cosmic microwave
background, and in the more modern universe measured with supernovae.
TLDR: the so-called Hubble tension is getting stronger.
Patrick Bryant offers some excellent clarification, pointing out that that the CMB number isn't
actually a "measurement" of the current rate of expansion - which of course it can't be
because that light comes from the beginning of the universe.
Instead, it provides us with an enormous amount of information about the composition and expansion
of the universe back then.
We then use our cosmological models to predict what the expansion rate should be today.
For example, based on the amount of matter and dark energy, we can figure out now much
the expansion should have slowed or sped up.
And the value we get is different to what we observe in the modern universe.
The tension could therefore be resolved by finding an error in either the CMB or supernova
measurements, but also by finding one of the assumptions in the CMB calculation is wrong
- which would force us to change our model of how the cosmos evolved.
That would be the most exciting case, in my opinion.
In might, for example, tell us that dark energy has changed over time - which might help us
figure out what dark energy actually is.
Max Graham asks how gravitational waves encode the distance that they've traveled.
Glad you asked! The intensity of light drops off with the square of the distance traveled.
If you know the true brightness, or luminosity, measuring the distance-dimmed brightness lets
you calculate that distance.
Trouble is you can't get that luminosity directly from the light by itself.
But it's different with gravitational waves from merging black holes.
The intensity or amplitude of those waves drops off with distance, not distance squared.
But the important thing is that the amplitude of the wave is directly encoded in the frequency
of the wave.
As black holes spiral towards each other, the frequency of the last phase of the inspiral
is pretty uniquely determined by the so-called chirp-mass, which is a combination of the
masses of both black holes.
But that chirp mass also determines the power that was radiated in gravitational waves during
the inspiral.
So, measuring the inspiral frequency gets you the power - which you can think of the
amplitude before it fades over distance.
So then the amplitude of the wave as we see it at Earth tells us how much distance the
wave must have traveled.
I said at the start of the episode that it's exciting for scientists to be proven wrong.
Hidden Marty offers this correction: Scientists love when OTHER scientists are proven wrong.
I gotta hand it to you, that's even more exciting, especially if those other scientists were
the ones saying that YOU were wrong.
But the point is that scientists do celebrate and embrace wrongness for the way it helps
point us towards increasing knowledge.
And it's really worth pointing out that this stuff is aspirational - the tendency to re-question
everything is hard baked into the scientific process.
Scientists are wrong a lot, but their wrongness is self-correcting.
Tumasch says Ugh, cosmology, I can't be bothered with YOUR crisis right now...
Tumasch, the beauty of science is that it brings us together.
Its crisis is everyone's crisis.
Whether it's a full blown existential crisis, or just a little radiating Hubble tension
in your neck from staring at too much supernova data.
Science, the great unifier.