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There is one interpretation of the meaning of quantum

mechanics that somehow manages to skip a lot of the wildly

extravagant or near-mystical ideas of the mainstream

interpretations.

It's the de Broglie-Bohm pilot-wave theory.

And despite its alluringly intuitive nature,

for some reason it remains a fringe theory.

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Misinterpretation of the ideas of quantum mechanics

has spawned some of the worst quackery pseudoscience hoo-ha

and unfounded mystical storytelling

of any scientific theory.

It's easy to see why.

There are some pretty out there explanations

for the processes at work behind the incredibly

successful mathematics of quantum mechanics.

These explanations claim stuff like things

are both waves and particles at the same time,

the act of observation defines reality,

cats are both alive and dead, or even that the universe

is constantly splitting into infinite alternate realities.

The weird results of quantum experiments

seem to demand weird explanations

of the nature of reality.

But there is one interpretation of quantum mechanics

that remains comfortably, almost stodgily, physical.

That's de Broglie-Bohm pilot-wave theory.

Pilot-wave theory, also known as Bohmian mechanics,

stands in striking contrast to the much more mainstream ideas

of, for example, the Copenhagen and

many-worlds interpretations.

Now we've covered both of those before.

And those episodes are really worth a look.

Pilot-wave theory is perhaps the most solidly physical, even

mundane, of the complete and self-consistent interpretations

of quantum mechanics.

But at the same time, it's considered

one of the least orthodox.

Why so?

Because orthodoxy equals radicalism plus time.

And the founding fathers of the Copenhagen interpretation

of quantum mechanics-- Niels Bohr and Werner Heisenberg--

were radicals.

When quantum theory was coming together in the '20s,

they were fervent about the need to reject

all classical thinking in interpreting

the strange results of early quantum experiments.

One aspect of that radical thinking

was that the wave function is not a wave in anything physical

but an abstract distribution of probabilities.

Bohr and Heisenberg insisted that in the absence

of measurement, the unobserved universe is only

a suite of possibilities of the various states it could take

were a measurement to be made, and that upon measurement

fundamental randomness determines

the properties of, say, the particle that would emerge

from its wave function.

This required an almost mystical duality between the wave

and particle-like nature of matter.

Not everyone was so sure.

Einstein famously hated the idea of fundamental randomness.

But to counter Bohr and Heisenberg there

needed to be a full theory that described how a quantum

object could show both wave and particle-like behavior

at the same time without being fundamentally probabilistic.

That theory came from Louis de Broglie, the guy who originally

proposed the idea that matter could

be described as waves right at the beginning of the quantum

revolution.

De Broglie's theory reasoned that there

was no need for quantum objects to transition

in a mystical way between non-real waves

and real particles.

Why not just have real waves that

push around real particles?

This is pilot-wave theory.

In it, the wave function describes

a real wave of some stuff.

This wave guides the motion of a real point-like particle

that has a definite location at all times.

Importantly, the wave function in pilot-wave theory

evolves exactly according to the Schrodinger equation.

That's the equation at the heart of all quantum mechanics

that tells the wave function how to change

across space and time.

This means that pilot-wave theory

makes the same basic predictions as any other breed of quantum

mechanics.

For example, this guiding wave does all the usual wavy stuff,

like form an interference pattern when it

passes through a pair of slits.

Because particles follow the paths etched out by the wave,

it'll end up landing according to that pattern.

The wave defines a set of possible trajectories

and the particle takes one of those trajectories.

But the choice of path isn't random--

if you know the exact particle position and velocity

at any point, you could figure out

its entire future trajectory.

Apparent randomness arises because we can't ever

have a perfect measurement of initial position, velocity,

or other properties.

But this hypothetical predictability

means that a pilot-wave universe is completely deterministic.

When de Broglie presented his still-incomplete theory

at the famous Solvay Conference of 1927,

it didn't go down so well.

Technical objections were raised and Niels Bohr

doubled down on the probabilistic interpretation.

De Broglie was convinced and he dropped pilot-waves altogether.

The idea was forgotten for decades

and Copenhagen became the orthodoxy.

It took until 1952 for another physicist, David Bohm,

to feel very uncomfortable with some

of the wackiness of Copenhagen and to rediscover de Broglie's

old idea.

Bohm took up where de Broglie left off and completed

the theory.

The result was Bohmian mechanics, also

known as de Broglie-Bohm pilot-wave theory.

These days, more and more serious

physicists are favoring Bohm's ideas.

However, it's far from being broadly accepted.

De Broglie himself remained firmly in the Copenhagen camp

even after Bohm's efforts.

See, although pilot-wave theory makes

all of the usual predictions of quantum mechanics,

it has some really fundamental differences.

Those differences are in the special thinking

you need to do in order to accept pilot-waves

over other interpretations.

In fact, most of the arguments for or against it

are about this special thinking.

Are you more or less comfortable with the oddness

of pilot-waves versus the oddness, say,

of Copenhagen or many-worlds?

So what uncomfortable thinking does pilot-wave theory require?

Well, for one thing, it needs a teensy bit of extra math that

mainstream interpretations don't.

As well as the Schrodinger equation

that tells the wave function how to change,

it also has a guiding equation that

tells the particle how to move within that wave function.

That "extra math" is considered un-parsimonious to some,

a needless added complexity.

However, the guiding equation is derived directly

from the wave function, so some would argue

that it was there all along.

A more troubling requirement of Bohmian mechanics

is that it does contain real complexity that is not

encoded in the wave function.

That's something that Niels Bohr was so fervently against.

Bohmian mechanics has so-called hidden variables,

details about the state of the particle that are not

described by the wave function.

According to pilot-wave theory, the wave function

just describes the possible distribution

of those variables given our lack of perfect knowledge.

But hidden variables have a bad rap in quantum mechanics.

Pretty soon after de Broglie first proposed pilot-waves,

the revered mathematician John Von Neumann

published a proof showing that hidden variable explanations

for the wave function just couldn't work.

That proclamation contributed to the long shelving

of pilot-wave theory.

But in fact, Von Neumann didn't quite get the full answer.

It turns out that the restriction

against hidden variables only applies

to local hidden variables.

So there can't be extra information

about a specific region of the wave function

that the rest of the wave function doesn't know.

This was figured out pretty soon after Von Neumann's paper

by German mathematician Grete Hermann,

although her refutation wasn't noticed until it was re-derived

by John Bell in the 1960s.

This helped the resuscitation of pilot-wave theory,

because Bohmian mechanics doesn't

use local hidden variables-- its hidden variables are global.

The entire wave function knows the location, velocity,

and spin of each particle.

This non-locality is another weird thing

you have to believe in order to accept pilot-waves.

Not only does the entire wave function

know the properties of the particle,

but the entire wave function can be effected instantaneously.

So a measurement at one point in the wave function

will affect its shape elsewhere.

This can therefore affect the trajectories and properties

of particles carried by that wave,

potentially very far away.

But quantum entanglement experiments

show that this sort of "spooky" action at a distance

is a very real phenomenon.

Again, we've gone into the non-locality

of entangled particles in detail before.

Also worth a look.

It's a tough idea to swallow, but experiments

indicate that some type of non-locality

is real, whether or not we accept pilot-waves.

It would be remiss of me to talk about pilot-waves

without mentioning the amazing analogy that

was discovered in bouncing droplets

on a vibrating pool of oil.

I'll let Veritasium cover this one in detail.

It's pretty amazing.

But we see many of the familiar quantum phenomena

appear in this macroscopic system of a suspended oil

droplet following its own pilot-wave.

Now, we shouldn't take a macroscopic analogy

as proof of microscopic reality, but it certainly

demonstrates that this sort of thing

does happen in this universe, at least on some scales.

I should probably also add that de Broglie-Bohm

pilot-wave theory is certainly wrong.

And I don't think anyone could deny that,

because it doesn't account for relativity,

either special or general.

That means it's at best incomplete.

While regular mechanics has quantum field theory

as its relativistic version, pilot-wave theory

hasn't quite got there yet.

Quantum field theory pretty explicitly

requires that all possible particle trajectories

be considered equally real.

Pilot-wave theory postulates that the particle really

takes a single actual trajectory, the Bohm

trajectory.

This is not consistent with quantum field theory,

and so there isn't a complete relativistic formulation

of Bohmian mechanics yet.

But there is good effort in that direction.

Now let's not even start talking about gravity--

no version of quantum mechanics has that sorted out.

Also, we can't ignore the fact that the initial motivation

behind pilot-wave theory was to preserve

the idea of real particles.

And I think we need to be dubious about that sort

of classical bias.

All that said, pilot-wave theory does

do something remarkable-- it shows us

that it's possible to have a consistent interpretation

of quantum mechanics that is both physical and

deterministic, no hoo-ha needed.

Maybe something like pilot-waves really do

drive the microscopic mechanics of spacetime.

Hey, guys.

So we recently launched our Patreon page.

And I want to thank those of you who have contributed so far.

This is really going to be a huge help.

And it's going to be a lot of fun.

I've loved the discussions we've been having

on the EM Drive and future episode ideas, not so much

the embarrassing quark compilation-- damn you,

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Anyway, if you're interested in supporting the show,

heading over to the Patreon page would be an amazing way

to do that.

Or, you know, just keep watching.

In our last episode, we talked about the strangest of stars,

the strange star-- aptly named.

Your comments, by comparison, were very reasonable.

Burak asks why quark/strange matter isn't found naturally

in the universe given that it's supposed to be so stable.

OK, so the hypothesis is that strange matter

is the most stable matter in the universe.

But this only applies when you have a large number

of quarks mushed together.

In that case, having one strange for every one

up and one down quark is a very low energy state and so

is very stable.

However, this doesn't work when there are only

a small number of quarks, say in the typical atomic nucleus.

In that case, any mass of strange quarks

will decay into the lighter up or down quarks.

But during the quark era, the universe

was full of this quark-gluon plasma.

And the problem is that the universe at this time

wasn't dense enough and was expanding

too quickly for strange matter to form in any great abundance.

That said, some strange matter made

have formed during the quark epoch.

And the resulting particles are called strangelets.

They may be around today.

Depending on the as-yet-unknown physics of strange matter,

these strangelets may even be expected

to be more stable the larger they are, and so would

grow over time.

In fact, such strangelets may even

convert any regular matter they come into contact

to into strange matter.

Sebastian Lopez asks how are the magnetic fields

of neutron stars created.

Well, to create and sustain a magnetic field,

you need some charge that's moving or spinning in some way.

That might seem a problem for an object made up

of neutral particles like a neutron star.

However, a neutron star isn't only made up of neutrons.

You have an outer crust of conductive iron

that can support an enormous current of electrons.

And below that crust, there's a region centimeters

to meters deep in which you have significant impurities

of electrons and protons mixed in with the neutrons, perhaps

up to 10% electrons and protons by mass of the star.

With their extreme rotation rates,

neutron stars support electric currents

sufficient for magnetic fields of up to 100 million tesla.

And then you have magnetars, which

are believed to get to 10 to the power of 11 tesla.

These fields are supported by superconduction of protons

beneath the surface.

The757packerfan would like to know where the neutronium

compares to adamantium.

I see where you've gone with this.

Neutronium pretty much sucks as a skeleton graft for Wolverine.

Firstly, it would weigh as much as a mountain

range, which isn't helpful.

Also, it's dense but not necessarily strong.

In a neutron star, it's a superfluid, so not ideal there.

But at atmospheric pressure-- or even

inside Wolverine pressure-- it would expand into a gas

cataclysmically and the neutrons would

decay to protons and electrons and an awful lot of radiation.

A five centimeter tube of neutronium

would explode with the equivalent

energy of around a trillion hydrogen bombs.

That's going to take some serious regeneration

to recover from.

By the way, this is why science is so important.

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