[MUSIC PLAYING] 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.

[MUSIC PLAYING] 12 00:00:31,590 --> 00:00:34,680 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.