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.