Neils Bohr said, “It is wrong to think that the task of physics is to find out how Nature is.
Physics concerns what we can say about Nature.” Well it turns out that if we pay attention to this
subtle difference, some of the most mysterious aspects of nature make a lot more sense.
What is physics really trying to do? Is it to find the mathematical laws that govern the universe?
Not quite - no one has to solve the Schrodinger equation in order for an electron to be able to do
its thing. Our laws of nature are just models. So maybe the job of physics is one step removed - to
come up with laws that do the best job at predicting how the universe works, and then hope
that we can infer truths about the universe based on which laws work best. But actually, some of the
founders of quantum theory were convinced that the role of physics was one step further removed
still. Neils Bohr insisted that what we actually model is the results of observation, not the world
itself. His student and closest colleague, Werner Heisenberg, put it well “The laws of nature which
we formulate mathematically in quantum theory deal no longer with the particles themselves but with
our knowledge of the elementary particles.” In other words, the mathematical laws of
physics don’t govern reality, they’re not even direct models of reality. Rather, the laws of
physics are models of our experience of reality. Physics models our information about the world.
In a recent episode we started talking about informational interpretations
of quantum mechanics. Then we discussed one of the more radical interpretations:
John Archibald Wheeler’s idea that information is really the most fundamental thing, and it
gives rise to the physical - a notion he pithily summarized with the expression “it from bit”.
Quantum mechanics tells us that asking questions of the universe radically changes how it behaves.
Wheeler followed that simple fact down the rabbit hole to what he saw as the logical
conclusion - the most fundamental existence is between the relationship between the observer and the observed.
Although he was careful to note that observer in this context didn't necessarily need to be conscious.
Wheeler may have been right, but we can explore the power of informational
quantum mechanics without committing to quite such a radical interpretation.
Today we’re going to see how a lot of the weirdness of quantum mechanics
can make sense if we think about it as a model of our information about the world.
Normally in physics we try to break up the world into its most elementary components.
We learn how those components behave, and see if we can rebuild the world from those parts.
In quantum mechanics, we have things like particles and fields which can only take on
discrete or quantized values. These quantum components also have weird properties like
fundamental uncertainty in their values and strange correlations between components
that we call entanglement. But as weird as quantum fields and particles are,
this still feels like a very physical way to define the building blocks of reality.
The physicist Anton Zeilinger has proposed an informational approach to quantum mechanics
in which the world is broken up not into physical parts, but into informational parts.
But what does it mean to use information as our building block? Information represents
our knowledge about the world. So our new building block becomes a statement about
the information we have — for example, about the location or speed or mass of a particle.
Zeilinger calls such a statement a proposition - it’s an answer to a question we could ask
about the world. He says that a quantum system is a collection of propositions.
A quantum system represents our knowledge of the world, not the world itself.
So how do you break up a “world” made of knowledge or information? Well, an informational building
block is the answer to a question. So the smallest informational building block is the answer to
a question with the fewest possible outcomes. Literally any answer can be reached by a series
of well-chosen yes-no questions. So Zeilinger says that any quantum system can be broken
into the results of binary questions. By insisting that the most elementary informational building
block contains only one bit - one yes-no answer - a surprising number of the weird results of
quantum mechanics suddenly make sense. Things like quantum indeterminacy, entanglement, and the
uncertainty principle turn out to be the expected behaviors of this sort of information system.
The simplest way to start is to look at a quantum system where the answer to a single
binary question seems to give a meaningful “physical” answer. Consider quantum spin.
From a physical point of view, think of it as a particle’s orientation - a spin axis that
can point either up or down. But really the quantum system is the answer to a question:
is the spin up or down relative to the direction of measurement? We ask this question with a Stern
Gerlach apparatus, where the magnetic moment of the particles interact with a magnetic field
gradient to deflect the particles either up or down, depending on the direction of the spin.
Let’s say we prepare an electron’s spin to all point up relative to our apparatus.
The spin contains one bit of information, one possible answer when we ask the electron what direction is your spin?
That answer is up.
But what if we asked the electron spin a different question “are you pointing
left or right?” We can do this by rotating the Stern Gerlach apparatus 90 degrees.
You started out with one bit of knowledge about the particle’s up-down alignment.
According to Zeilinger, by definition, that’s all the information that the elementary quantum
system of spin can contain. That means the left-right orientation is undefined. It’s
in a superposition state of both left and right until it’s measured. Run it through
our horizontally aligned Stern-Gerlach divide and the electron has an even chance
of being deflected left or right - its undefined left-right spin chooses randomly between the two
because it contains no information about its spin in that direction. And following that measurement,
the left-right alignment of the spin has become defined - after all, the electron has to come
up with an answer to the question you asked. But now with the left-right alignment defined,
our single bit of spin information is used up. The up-down alignment becomes undefined. So
by thinking of quantum systems as being made of these elementary “quanta of information”,
we see the indeterminacy of quantum theory arises naturally. Zeilinger even managed to derive the
equivalent of the Schrodinger equation by asking how quantum information should evolve over time.
Quantum entanglement also fits this picture. When we prepared our electrons to be spin-up,
that spin was relative to a chosen direction - the vertical in this case. But we could also prepare
an electron to have a spin direction that’s defined relative to another particle’s spin.
For example, a pair of electrons could be prepared that have opposite spin to each other.
Now remember our requirement that the spin of each electron can only contain one bit of information,
and that bit is taken up to describe its relationship to its partner electron.
Now the information is no longer isolated in the single electron’s spin, but rather spread between
two electrons. Two electron spins contain two bits, but those bits are distributed non-locally.
If you ask the spin direction of either of those electrons relative to your Stern-Gerlach
apparatus, you’ll learn the spin direction of both particles. And in making that measurement,
you’ve forced the single bit of spin information in both electrons to become defined relative to
your apparatus - whichever way you chose to align it. Our distributed information becomes
local to each electron, and in the process appears to force an instantaneous communication
between the particles - a spooky action at a distance. This is entanglement.
So we’ve seen how an elementary quantum system’s information content has to exist with respect to a
certain type of question that you ask of it. Spin direction in the last example. This idea leads us
naturally to some other staples of quantum theory - like the Heisenberg uncertainty principle.
In a previous episode we saw how the uncertainty principle arises from the limited knowledge that
we can extract from a quantum wavefunction. For example, that the product of the measurement error
in a particle’s position and momentum has to be greater than the Planck constant divided by 4-pi.
In fact, by bringing to bear the tools of information theory
we can derive an even tighter uncertainty relation - something known as entropic uncertainty.
This approach uses the informational definition of entropy - Shannon entropy - which is a measure
of the number of yes-no questions needed to extract all the information from a system.
The resulting “entropic uncertainty” has been used to explain one of the
original and most mysterious features of quantum mechanics - wave-particle duality.
This was demonstrated in by a team of physicists in 2014.
They applied entropic uncertainty to analyze Wheeler’s “delayed-choice” experiment. This
experiment causes a photon to behave like a wave or a particle depending on the question asked
of it. And that question could be asked after it passes through the experimental apparatus.
If it’s a wave it travels both paths of the device, if a particle it must only travel one.
Applying the notion of entropic uncertainty to the situation,
the team said that the wavefunction contained only one answer to two complementary questions:
just as our particle could only tell you if it was up or down, but not left or right,
the wavefunction of the photon they considered could tell you either which path the photon took,
or the phase of the photon by looking at the interference pattern.
Because of the finite information content of the wavefunction, it didn’t have answers
to both questions. So, they found that the wave-particle duality of quantum mechanics
arises from the limited information, the inability to answer two complementary questions:
“Are you a particle?” And “are you a wave?” at the same time.
It’s one thing to use quantum information theory as a mathematical tool, but quite another to claim
that information is somehow a more fundamental than the tangible stuff that most people
believe to be the building blocks of reality. In quantum mechanics, we tend to think of the quantum
wavefunction as pretty fundamental. It describes the evolving distribution of probabilities for
the results you might get if you tried to measure the properties of a quantum system.
Zeilinger and supporters would say that the wavefunction does not have a physical
existence independent of the observer. Rather, the wavefunction and the math that governs it
describe our information about the universe, not the universe itself.
But, if the wavefunction is about the information content of a system,
again, we come back to the same question that plagued Wheeler: “whose information?”
This same question haunted Einstein. Einstein famously once asked whether proponents of these
observer-centric interpretations truly believe the moon isn’t there when nobody looks. To this,
Bohr and Wheeler and Zeilinger and their supporters might say, “You can’t prove that it
is.” To learn about something necessarily involves an observer who is acquiring this knowledge,
so all we can ever know about the world is how we interact with it. Whether there is an
observer-independent world out there, we, being observers, can never prove. And it turns out that
a lot of the weirdness we see in the quantum world make more sense if we pay attention to the fact
that our only direct experience is with an entirely informational space time.
Look, the universe almost certainly is not a simulation. But you can’t be too careful. If you agree and
would like to spread the word, or if you just find this t-shirt amusing, you can pick one up
at pbsspacetime.com, along with the rest of our merch. Link in the description.
OK, In the last episode we talked about the formation history of the Milky Way, told through
the various acts of galactic cannibalism performed by our galaxy. Let’s see what you had to say.
Martijn van Oosterhout asks what happens to the central black holes of galaxies that the
milky way eats. The answer is simple - the Milky Way’s central black hole eats those black holes.
Eventually, anyway. If the swallowed galaxy is big enough to have its own so-called supermassive
black hole, that black hole will end up in some orbit within our galaxy’s gravitational well.
It’ll interact with stars, kicking them up to higher orbits while its own orbit decays. In this
way it’ll spiral towards the center and eventually merge with our own supermassive black hole,
making it supermassiver. This is one of the main ways that supermassive black holes grow.
Erik Ziak asks how galaxy interactions affect the galactic habitable zone,
suggesting that it may be less of a zone and rather a more complex region.
Erik is referring to the recent episode where we talked about what parts of the Milky Way
could potentially host life based on various factors like abundance of necessary elements
and there not being too many supernovae. The galactic habitable zone is defined to be a
ring around the disk, not too close to the core and not too far out. It may be that there are
better and worse parts of this ring, but remember that a star will move through many different
regions as it orbits the galaxy. It’ll be born in a spiral arm probably, and then move in and out of spiral
arms every hundred million years or so. It’ll dip above and below the plane of the disk slightly.
Life on Earth has persisted for billions of years, so it’s survived various regions - although it may
be that mass extinction events correlate with entering more dangerous regions of the galaxy.
David Kosa asks about actual collisions between stars when galaxies merge. Given that most of the
galaxy is empty space, what’s the probability of stars colliding? Well for any given star
the chance is very small - given that stars are of order a light-second across, while the
distance between them is light years. I’ve heard an estimate for the number of stellar collisions
that are expected to occur when the Milky Way and Andromeda collide - out of the trillion-ish stars
involved in the merger, expect approximately one collision. And what happens to the stars in that
collision? It depends on how head-on the collision is, and the mass ratio between the stars.
Glancing collisions can result in stars merging, which increases the mass and also rejuvenates the
star because more hydrogen fuel gets pumped into the fusion core. It’s believed that the oddly blue
stars at the cores of globular clusters may have resulted from stellar mergers in these hyper-dense
bundles of stars. On the other hand, head-on collisions tend to disrupt stars. For example,
its been shown that a more compact star punching through a more diffuse star will accelerate fusion
in the core of the latter, causing it to blow itself to pieces. I know of at least one case
where this is believed to have happened due to a black hole or neutron star impactor.
At the end of the last comment responses I misinterpreted a couple of comments that said that
the expansion of the universe could be thought of as matter shrinking rather than the universe
expanding. I took those comments as being humourous - but probably I was projecting because I sometimes feel
the temptation to give very plausible nonsense when someone asks for an explanation.
At the american museum of natural history for example there’s a mammoth skeleton and right next to it a tiny
bronze model of what the animal is thought to have looked like. I’ve convinced quite a few people
that the model represents the pygmy mammoth that lived at the same time as its gigantic cousin.
I always correct the misinformation afterwards, but it’s hard to resist the joke. Sorry if I
misinterpreted the comments. It is actually an interesting question: why can’t matter be
shrinking instead of the universe expanding? In terms of the relative scale of distances and sizes
the two are identical. However a number of things would have to change in concert for matter to be shrinking -
in particular the strength of the various forces. Yet to expand space you just need to change space,
and general relativity predicts that this should happen. Also, we wouldn’t expect cosmological
redshift if matter is shrinking because there’s no stretching of the traveling photons. And finally,
in a universe where galaxies shrink you’d expect pygmy mammoths, which I’ve already told you don’t
exist. Instead we see the gigantic mammoths the type predicted by the expanding universe model.