Why the “Wave” in Quantum Physics Isn’t Real

Transcript

When people do a study of, for  example, the double-slit experiment,   and they approach the double-slit experiment  in the traditional way, one particle at a time,   a wave function that we can pretend  is moving in three-dimensional space,   but this is really just an artifact of the  fact that configuration space for one particle   looks three-dimensional.

It looks like you  should treat the particle as a wave as it   goes through the slits to get the correct pattern  over many repetitions of landing sites. You know,   we don't actually see a wave on the other side.  What we see is dots, many, many landing sites   over many repetitions of the experiment.

The  wave is inferred. But when you measure where   the particle is at the end of the experiment,  or you measure which hole it goes through,   you get a definite result, and that makes it  look more like a particle.

So there's this idea   that sometimes things are particle-like and  sometimes they're wave-like depending on what   feature of the system we're trying to study.  This became known as wave-particle duality.   This is further complicated by the fact that  there are waves of a different kind in physics.   Electromagnetic waves, for example. Light is a 

disturbance in the electromagnetic field that   propagates like a wave through three-dimensional  space. And those are waves. I mean, like I said,   I teach Jackson electromagnetism. We talk about 

waves moving through three-dimensional space.   It's very easy to confuse the waves of a field,  like the electromagnetic field, with the wave   functions or Schrodinger waves of quantum  mechanics. But they're not the same thing. And   this has bled into the wave-particle duality.

When  Planck in 1900 and Einstein in 1905 and various   people were proposing that light came in quanta,  discrete particle-like quanta called photons,   the wave that they were imagining was the wave  corresponding to photons was a three-dimensional   electromagnetic wave, a wave of the familiar  kind of wave.

The wave functions that Schrodinger   introduced in 1926 were not like those waves.  They were not three-dimensional waves in physical   space of a field. They were these abstract,  complex-valued functions in a high-dimensional   configuration space. And when you measured them, 

they collapsed. Now, if you're in an MRI machine   and they've turned on a very strong magnetic  field, you don't have to worry that if you do   the wrong measurement you're going to collapse the  magnetic field in the MRI machine. It's not that   kind of field.

The waves they're beaming at you  are not those kinds of waves. So you have to make   a distinction between the old waves, the waves of  a field, and Schrodinger waves. And I want to make   super clear that in the indivisible stochastic 

approach to quantum mechanics that we've been   talking about, I'm saying Schrodinger waves are  not real things. These abstract things that live   in this high-dimensional configuration  space, those are not physically real.   But classical waves or the waves of a field, which  are a different, conceptually different kind of a   wave, those are perfectly valid.

And if you're  studying a system that's not made of particles   but a system made of fields, you're going to  see wave-like behavior as well, but those are   a different kind of wave. And these are the kinds  of subtleties that I think get lost when someone   just says wave-particle duality.

So again, just  to summarize, the relationship between a photon,   a particle of light, and an electromagnetic  wave is not like the relationship between an   electron and a Schrodinger wave function for  the electron. Now what makes this even more   confusing is that electrons do have fields also. 

There's a so-called Dirac field that plays a very   important role in the standard model. And this  is a field, a field in three dimensions for the   electron. But the Dirac field for the electron  is not the Schrodinger wave for an electron.

So   these are super subtle distinctions, but it's  important to keep them in mind. What makes   it even more confusing is that particles like  electrons, which are called fermions, these are   particles that have an intrinsic half-integer  spin.

They're the particles that obey a Pauli   exclusion principle. You can't put them all in the  same energy state. They make chemistry possible by   not having all the atoms collapse at the ground  state.

Electrons are like this, quarks, protons,   neutrons. Although they have fields associated  with them, the fields associated with them are   not classical fields like the electromagnetic  field. The fields are much more bizarre and weird.   And I'm not gonna have time to talk very 

much about them except to say that one of the   limitations of Bohmian mechanics is that it has  a great deal of difficulty dealing with the kinds   of fields associated with fermions. And that's  one reason why Bohm mechanics has difficulty,   the Bohm pilot wave theory. I'm getting way ahead 

of myself, but I just wanted to just clarify   what's going on in wave particle duality. So in  the indivisible stochastic approach, there are no   Schrodinger waves as part of the fundamental  physics. Of course, you can, when you go to   the Hilbert space picture, you can mathematically 

write down wave functions and use them, write down   Schrodinger waves, but they're not physically  there. You don't need them to explain the   interference patterns. The indivisible stochastic  dynamics itself generically predicts that you'll   have what look like over many repetitions of the 

experiment, dots that look like they're following   some kind of wave equation. But there is no wave  actually involved in those experiments. But I'm   not saying that field waves, the waves in fields  are not there.

That's a different kind of wave.   So speaking of these waves, you mentioned quantum  field theory indirectly with Dirac. Does your   approach illuminate any aspect of quantum field  theory or the standard model? We've been talking   about quantum mechanics, sure, especially in part  one and part two.

What about QFT? Yeah. So one of   the nice things about Bohm's pilot wave theory  is that it works really beautifully for systems   of fixed numbers of finitely many non-relativistic  particles. That's a lot of qualifications.

Doesn't   work so easily for fields. You end up either  having to do very complicated things or maybe even   reducing stochasticity of some kind. It gets kind  of messy and there's a lot of difficulty handling   fermionic fields in particular, the fields 

associated with particles like electrons. One of   the advantages of this approach is although, okay,  so let me just say something very quickly about   Bohmian mechanics. Now this is different because  this is also related.

In Bohmian mechanics for,   again, systems of fixed numbers of finitely many  non-relativistic particles, we have deterministic   equations. There's a pilot wave that guides  the particles around. The wave function, the   pilot wave obeys the Schrodinger equation.

Then  another equation called the guiding equation is   how the wave function, the pilot wave guides the  particles around. And everything is deterministic.   There's no fundamental probabilities. There 

are some initial uncertainties in the initial   configuration of the system. And these evolve to  become the Born rule probabilities later. But the   dynamics is fundamentally deterministic and is  not generating the probabilities in a fundamental   law-like way.

This picture is in some ways very  elegant, provided you're okay with a pilot wave   living in a high dimensional configuration  space. Although I should say that Goldstein,   Durer, and Zanghi have already proposed the idea  that the Bohmian pilot wave is law-like and not   a physical thing.

So there are other ways to read  this theory. The problem is it helps itself to a   lot of very special features of models that  consist of fixed numbers of finitely many   non-relativistic particles. Features that are 

unavailable when you go to more general systems   like fields. So you end up having to write down  a very different looking model, including in some   cases models that you need to now deal with  stochasticity and indeterministic dynamics.   And they just don't really work very well when  you try to go beyond.

One of the other things   that Bohmian mechanics requires is a preferred  foliation of space-time. So last time we spoke   we talked about how in special relativity there's  no preferred way to take space and time and divide   it up into moments of time, like different ways  to do it.

The guiding equation, the equation   that takes the pilot wave and explains how the  pilot wave, obeying the Schrodinger equation,   how the pilot wave guides the particles  around, they call the guiding equation,   depends on there being a preferred foliation  of space-time, a slicing of space into moments   of time. That's also not really great.

It  works fine in the non-relativeistic case,   but we want to do relativistic physics like we  often do when we want to do quantum field theory,   which is the kind of models we use when we want to  deal with special relativity and quantum mechanics   together, as in the standard model. Preferred 

foliation is really difficult to deal with,   not impossible, but it'd be nice if we didn't  need it. In the indivisible stochastic approach,   there's no guiding equation. There's no pilot  wave.

It's not that you solve the Schrodinger   equation, get a pilot wave, and then take the  pilot wave and plug it into a guiding equation,   which depends on a preferred foliation and then  the guiding, none of that happens. There's just   the indivisible stochastic dynamics, which  can be represented in Hilbert space language,   but the dynamics is just directly happening. 

There's no middleman. There's no pilot wave   and guiding equation in the middle. This means  the theory is not going to be deterministic. I   think one question in the comments is, is 

this fundamentally deterministic or not?   It's indeterministic. It's not a deterministic  theory, but because there's no guiding equation,   there's no preferred foliation. Because we're  not relying on all these special features of   the particle case, it's perfectly easy to now 

generalize this to more general kinds of systems.   Have you done it? Have I done it? Good question.  There's this thing called time. Time is bounded   and limited. Is it? It is, amazingly. In your 

framework? At least in my life. Okay. And when   we get to open questions like research directions,  which maybe people watching this may be interested   in because, I mean, the best part of a new  formulation or picture or model or whatever is,   are there things people can work on? There are 

things people can work on. This is one of the   things people can work on. So it is, the term here  is straightforward in principle to generalize this   to quantum fields because there's no, none of the  obstructions are there like they were before.

One   of the problems with Bohmian mechanics is  your wave function has to live in a space,   configuration space. And fermionic particles don't  have a familiar kind of configuration space. This   is what makes it so hard to do Bohmian mechanics. 

But there's no pilot wave here so you just don't   even have that obstruction. So many of the things  that would have obstructed us from just applying   this to any kind of system are just, they're just  not there anymore. So if you want to deal with a   field theory, you just replace particle positions 

with localized field intensities. These become   your degrees of freedom. And then you just apply  the stochastic laws to them and it works the usual   way. The problem with quantum field theory is 

that quantum fields in general is that they have   infinitely many degrees of freedom, infinitely  many moving parts. At every sort of point in space   in the most sort of, you know, I mean, this is  a whole renormalization story of effective field   theory. But like at a simplest sort of like bird's 

eye view, you have a degree of freedom at every   point in space, infinitely many of them. And this  makes them very mathematically difficult to deal   with. Even in the traditional Hilbert space or  path integral formulation, quantum field theories   are really mathematically tricky.

And there  are very few, if any, I think there are none,   rigorously defined quantum field theories that  are also empirically adequate. Like none of the   quantum field theories that make up the standard  model have been rigorously defined.

This means   that anytime you mention quantum field theory,  you're going to run into mathematical difficulties   that are just because quantum field theory is  mathematically very complicated. So I think   there's a research direction for an enterprising  student to not only formulate quantum field theory   in this language, but also see does it make any 

of the mathematical difficulties easier? Do any of   them become harder? Like what exactly does it look  like when you do this super carefully? And that's,   I would say, an open research question. But  many of the obstructions that are in the way in,   for example, Bohmian mechanics are no longer in  the way here.

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