Thank you to Wren for supporting PBS. In the world of quantum mechanics, it’s
no big deal for particles to be in multiple different states at the same time, or to teleport between locations, or to influence each other faster than light. But somehow, none of this
strangeness makes its way to the familiar scale of human beings - even though our world
is made entirely of quantum-weird building blocks. The explanations of this transition
range from the mystical influence of the conscious mind to the grandiose proposition of multiple
realities. But there’s one explanation that feels as down to earth as the classical world
that we’re trying to explain. Let’s see if it actually makes sense. In quantum mechanics, particles don’t have definite properties. Rather they are described by something called the wave function. In fact, a particle is its wave function: a fuzzy distribution of possible properties that only
become sharply defined in particular circumstances. For example when we make a measurement of
a particle, the property that we’re measuring seems to be plucked from the wide range of
possible values defined by the wave function. We say that the wave function collapses - it
appears to shrink to a window whose narrow width is defined by the precision of our measurement. A famous example of this is Schrodinger’s cat. A scientist puts a cute kitty in a closed box with a radioactive atom attached to a
vial of poison gas. The atom has a 50-50 chance of decaying, triggering the release of gas
and so killing the cat. Prior to opening the box, from the scientist’s perspective the
atom’s wave function exists in what we call a superposition of states. It is simultaneously
in a state of decayed and not-decayed. So then, is the cat also in a superposition of
dead and alive? Honestly, probably not. At some point between atom and cat the fuzziness
of the atom’s wave function collapses into one of the two states. And becomes or. Decayed
and not decayed becomes decayed OR not, and the cat is alive or dead, not alive and dead.
The quantum becomes classical at some point between the subatomic and the macroscopic. The idea of wave function collapse was first
proposed by Werner Heisenberg, one of the principle founders of quantum theory. Heisenberg
and his friend Neils Bohr were convinced that this wave function collapse was real. It’s
a central part of their Copenhagen interpretation of quantum mechanics. But neither physicist
claimed to know where or how wave function collapse actually happened. And fair enough,
because it’s confusing. Quantum superpositions can involve many quantum particles. So how
far can the superposition extend? The atom, the radioactive detector, the vial of poison,
the cat, the scientist? Opinions on the matter span all extremes.
John von Neumann and Eugene Wigner thought that wave function collapse happens at the
instant of subjective awareness - in other words, they thought that consciousness collapses
the wave function. At the opposite end of the spectrum, many physicists believe that
the collapse of the wave function is a fiction. For example in Hugh Everett’s Many Worlds
interpretation, the wave function never collapses, rather lasts forever, splitting into parallel
realities. And we have the idea of quantum decoherence, where different parts of the
wave function simply become unable to interact with each other. We’ve discussed all of
these ideas in the past. We also have de Broglie-Bohm pilot wave theory, where particles already
have defined properties that are hidden within the wave function. The wave function may collapse, but particles maintain a rigid physical nature. We've discussed all of theses ideas in the past. But today we’re going to look at a different approach to collapsing the wave function. One that accepts the wave function as the
fundamental building block of reality, unlike pilot wave theory. And one which avoids multiple universes by insisting that collapse does really happen. But it also avoids mystical-seeming
explanations like consciousness-induced collapse. Our story starts in 1986 when three Italian
physicists, Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber published a paper that outlined
what was to become known as GRW theory - the first in a new class of alternate quantum
theories called “objective collapse theories. In objective collapse theories, wave functions
are real, physical entities that literally collapse when they’re measured. But the
collapse has nothing to do with a conscious observer or any subjective explanation.
The wave function and the collapse are completely real, completely objective — hence the name. To understand how objective collapse theories
work, we need just a little more quantum mechanics. The behavior of the wave function is described
by the Schrodinger equation, which tracks its evolution through space and over time. As we’ve discussed previously, the Schrodinger
equation is a linear equation - which just means that if you add together solutions to this equation, the result is also a solution to the equation. This is part of what makes
superpositions possible - it allows different parts of the wave function corresponding to
different possible measurement results to evolve independently of each other. Another thing about the Schrodinger equation is that it’s time-reversal-symmetric. Running it
forwards generates future states, but running it backwards lets you perfectly recover the
past states. When wave function collapse happens, different
parts of the wave function interact with each other instantaneously and non-locally and
non-reversibly. This means that wave function collapse is a non-linear process and it’s
non-reversible. It’s not part of the math of the Schrodinger equation. So to model the effect of wave function collapse,
Ghirardi, Rimini, and Weber added a non-linear term to the Schrodinger that could cause this
wave function collapse in just the right way to explain why subatomic systems could be
quantum but large systems were always classical. Think of this non-linear action as a rare
and random hit that the wave function takes at a particular location. That hit causes
it to collapse to a particular value. And when it collapses, it immediately collapses
all parts of the wave function that it’s connected to. The key to making this work is that these
hits are very rare. It’s incredibly unlikely that a single isolated quantum particle will
undergo collapse during the course of an experiment. But the more particles you add, the more likely
that one of them experiences collapse, and that single single event collapses the wave
function of the entire system. Any attempt to measure an isolated quantum system necessarily means bringing lots of particles into the picture - in the measurement device and in
your own brain. With enough particles collapse becomes inevitable. So this “hitting” mechanism gives a potential explaination for the quantum-classical divide - it simply depends on the number of particles
involved. Small things can stay quantum, but the chance of collapse to classicality increases
with size, and big things are essentially never quantum. GRW suggested that the collapse rate should
be about 10^-16 hits per second per particle. With this value, a single particle wave function
remains uncollapsed for around 100 million years. But if you have Avogadro’s number
of particles - the 6x10^23-ish of a macroscopic object, you expect a collapse every 10 nanoseconds or so. GRW was a revolutionary theory that inspired
many subsequent models, like Continuous Spontaneous Localization. In CSL, physicists imagined that the localizing mechanism was a randomly jiggling field, like the frenetic Brownian motion of
pollen grains floating on water. Matter’s interaction with this fluctuating field would
continuously collapse the wave function, in contrast to the discrete and violent hits
of GRW theory. But neither of these models really tried to
explain what the mechanism actually was. They just thought there was some mysterious field that interacted with all matter — almost like it was a fifth fundamental force. But
Lajos Diósi and later, Roger Penrose, saw no need for some new fundamental force. They
thought nature already gave us a perfectly good source of wave function collapse: gravity. Gravitational decoherence would simultaneously
explain two mysteries of physics. 1. What causes the transition from quantum to classical?
And 2. Why can’t gravity be quantized like the other forces. All of the collapse models
attempted to answer point 1, but only Diósi and Penrose’s model could answer 2: gravity
can’t be quantized because gravity isn’t quantum. They proposed that gravity and the
three quantum forces are diametrically opposed. Quantum mechanics rules when things are small,
but add enough mass, and the gravity of the system will cause it to rapidly decohere into
a classical object. Instead of gravity being quantized, Penrose’s theory predicts quantum
mechanics will be “gravitized.” For example, consider a massive object. General
relativity says that the mass from that object will warp the space-time around it. But quantum
mechanics says that this object can be in a superposition of two locations, where it
is both “here” and “there” at the same time. Put these two facts together, and
you will get a superposition of two different geometries of space-time. According to Penrose,
this isn’t possible. The instability introduces a nonlinear term in the Schrödinger equation,
causing the wave function to rapidly and randomly choose to make the object appear either “here”
or “there,” but not both. Because each of these objective collapse models
involve modifications to the Schrödinger equation, they are not mere interpretations
of quantum mechanics — they are distinct theories with unique predictions. This means
that, unlike other interpretations we’ve discussed — for example, Bohmian mechanics
or Many Worlds — objective collapse models can actually be tested. Some tests have already ruled out some of the models and placed restrictions on the nonlinear parameters of others. Direct tests of collapse models would involve
putting a macroscopic object in a superposition of being “here” and “there,” then
measuring how long it takes for the superposition to collapse. This time should be proportional
to the size of the object. Experiments are approaching the masses necessary to make such
direct measurements, but they’re not quite there yet. Instead, physicists have come up with clever ways to look for other, indirect signs of collapse models. For example, the models imply that a quantum wave function will be randomly tossed about and jostled by gravity or some other collapsing field. If the quantum object happens to be electrically
charged, then the constant jiggling and acceleration caused by this Brownian motion means it will
emit radiation. Last year, scientists working in Trieste, Italy tried to measure this radiation
effect. They put an 8-by-8 cm germanium crystal in a cryostat and carefully measured the amount
of radiation it emitted. The predicted effect was so tiny, researchers
had to go underground to try to minimize as many background sources as possible. In the
Gran Sasso laboratory, a main source of noise, cosmic muons, was reduced by a factor of nearly
1 million. Then, they further shielded the crystal with layers of copper and lead. With
such pristine conditions for a high-precision measurement, the scientists in Trieste were
able to measure single photons emitted from the germanium crystal. After watching the crystal for two months,
they had detected a grand total of 576 photons. Now this isn't enough to confirm or refute the general idea, but the scientists were able to place tight restrictions on the value of the free parameters in the
Diósi-Penrose model. It even ruled out Penrose’s original version of this model. There are still many candidates for objective
collapse models that have not been ruled out by experiments, so stand by for a jubilant
confirmation or a sheepish “never mind”. Whatever the case, it’s exciting that there
are real and accessible experimental paths to investigating one of the biggest unanswered
questions in physics. And one that we’ll be coming back to. What, in fact, is the quantum
wave function? And how does this abstract system of shifting realities give rise to
our solid, familiar, and singular space time. Thank you to Wren for supporting PBS. Wren
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climate projects at Wren.co Before getting to comments, we’d like to
thank our supporters on Patreon - we couldn’t do this without you. Today though we also want to give an extra special thanks to Ben Dimock who’s supporting us at the Big Bang Level.
Ben there are many uncertainties in the world of physics. Is the wave function objectively
real? Or is it a statistical or subjective fiction? Did I measure position precisely
or was it momentum? Who put my cat in that funny box, and why isn’t he purring any
more? But amid all this uncertainty it’s a powerful thing to know for sure that our
science bills will get paid this month. Ben, thank you for collapsing our wave function
in the direction of making more space time. Last time we tackled a question of utmost
gravity. Literally. How does gravity itself escape the inescapable gravity of a black
hole. The BuzzBen asks what happens when gravitational waves pass through black holes. Is there gravitational lensing? Well that’s exactly right. Gravitational waves have to move along the same fabric of spacetime as everything else. After all, they are wiggles in that very fabric. So they get deflected by gravitational fields just like
anything else. If that gravitational field is made by a black hole then the result depends
on how direct the hit is, and on the relative size of the black hole and the wave. A gravitational wave whose wavelength is short compared to the black hole’s event horizon can be completely
swallowed, while a larger gravitational wave will get deflected and partially absorbed. The
absorbed energy can go into changing the black hole’s velocity, but also can be added to
the black hole’s mass. BuzzBen’s also asks whether it’s possible to focus gravitational
waves to a single point to create a black hole without mass. The answer is again yes.
Just as it’s possible to create a black hole from pure light - a so-called kugelblitz
- if you could focus enough energy from gravitational waves into a small enough region of space
you could actually make a black hole from those waves alone. Ryan R asks how we can know that a black hole’s
mass has time to crush down to the singularity, given that time dilation slows the event down during the collapse. So this is a confusing point. The time dilation that we talk about approaching
the black hole event horizon is not from the point of view of falling matter, but from
the point of view of a distant observer. Only the distant observer sees matter approach
a state of frozen time, and you’re right that from that person’s point of view the
singularity - in fact the entire event horizon, never quite finishes forming. But from the
perspective of the falling matter it most definitely forms, and it is definitely squished
- though whether it’s to a singularity or not is still not really known. On that note Pesila Ratnayaje asks if an outsider
observer sees matter slow and freeze at the event horizon, what happens when the event
horizon grows? Does that matter get swallowed up? This is tricky because that the definition of the event horizon is also tricky. In an idealized black hole, the event horizon is defined from
the perspective of an observer at “infinite distance” - aka very very far away, which is after all where you wanna be relative to a black hole. The event horizon is that surface around the black hole
below which no sub-lightspeed object can escape. And by escape I mean reach YOU at your “infinite
distance”. And it’s the surface from which light is infinitely redshifted - sapped of
all energy - before it reaches that infinite distance. We observe an object being frozen at the event
horizon if the light emitted at the moment it crosses the horizon from its perspective
takes infinite time to reach us. So to lose an object beneath a growing black hole means
that the event horizon envelopes that final photon, not the object. By some definitions
of the event horizon that actually never happens. And so everything that went into the black hole remains frozen on the horizon. But to understand why were’ really going to need a whole episode. Chillyman145 asks a related question, but
now it’s for black holes that shrink due to Hawking radiation. This is a lot more speculative. Some physicists think that the Hawking radiation actually carries away the information from
previous infalls. And we actually already have an episode on that one. Check out our
episode on the black hole information paradox for the full speculation. Lucas Thomas asks another related question.
If we never see anything cross the event horizon, why do we say information is lost? When people
talk about information being lost in a black hole, they’re usually referring to the fact
that lots of information goes into building a black hole, but in its formation, but in its original formulation Hawking radiation is supposed to be completely random - information free
- and so that when a black hole evaporates all the information that went in is gone. And this is the black hole information paradox that I mentioned. And I'll refer you to that episode for more answers. dannymac63 likens Space Time to a black hole, in which it’s captivating and radiates information constantly. Well thank you dannymac63. But
remember, we don’t know whether black holes radiate actual information. It could be that
they, and so by your comparison, this show, only suck in information, and radiate nothing
but nonsensical noise. Which of the two is the case might be relative to the observer.
For example Siderite Zackwehdex loves how we ask questions a kid would ask then answer
in a way they can barely comprehend. So…. “Barely” comprehend means you comprehended
a little bit, right? I’ll take it as a win.
